Something like Maharraqa, for example. The southernmost point of the Empire. Would people coming from the south be fought? Would there be an inspection process that could allow them to enter the Empire?
The first thing to think about Roman 'borders' (henceforth the limes) is that they are generally less of a defined line, and more of a zone of control. So for example, although Hadrian's Wall might be thought of at some points as a northerly limes, there are forts beyond it and patrols regularly will go out on both sides. It's not a fixed line behind which Roman soldiers sit and wait for the "barbarians" (which is a concept I don't have time to unpack right now) to show up.
The core of this is essentially the question: what were the limes for? Certainly in the case of Hadrian's Wall (which I'm going to talk about most because I know it best), it's generally accepted that it's not a reasonable defensive structure (although at points, some spectacular use of natural stone outcroppings makes it extremely defensible) and that any attacking force would quickly overwhelm a specific point. This is evidenced by it only being (apparently) seriously attacked from the north and having people break through a few times - in 180, and again in the 360s.
So there are a few arguments to be considered: firstly, that (like later dykes) they're there to slow down the smaller raids which are most likely to occur. Hauling stolen animals or goods over that sort of structure, or across the Danube, is going to be difficult. Someone attacking from over it will have to go to one of the deliberate gaps in the wall, or spend significant time demolishing part of it, which is a tough job, and every hour is an hour where the garrison is more likely to catch up with you.
The second is that they're there to essentially control traffic through that area and act as a monument to the power of the state, which is the same idea but a little bit less violent. If you're hauling grain from the north to the south or vice versa, you have to pass through the zone of control and go to a specific point where you can pass, mostly through some small fort or border post. You have to interact with soldiers, and possibly pay some sort of customs tax. If you want to visit family on the other side - and there definitely were people who were split between sides of it because this is an arbitrary thing that went up relatively quickly (some parts of the wall even have ploughmarks underneath the construction) - you can't just stroll over, you still have to go through a border crossing. It's even possible some people were travelling through it every day to access agricultural areas. Some people have made analogies with the Indian salt hedge or with the barrier between Gaza and Israel.
The third is as an early warning signal; this is particularly relevant to limes which did not have a wall or palisade. Although they could not in any way stop a significant movement of people or an army they could send warning that this was happening and have a larger force show up to handle it.
In terms of what life was like on the frontiers, it was extremely variable - we're talking about a huge swathe of places over an awfully long period. In Britain, it led to a local economy that was centered around the needs of soldiers, e.g. food, pasture, sex work, armour and weapons, etc. Markets turned into small (and sometimes larger) towns or vici around forts and other towns were set up as colonia by retiring soldiers. Simply having that many soldiers likely distorted the local economy and landscape to cater for them in a way that was quite different to the normally relatively ungarrisioned interior.
However, it's hard to determine what life was like for most ordinary people on the border. Beyond the famous Vindolanda letters, which were preserved only by complete accident and which showcase a very specific view in a very short period, there's relatively little written material from Hadrian's Wall (Britain in general is not great for written records from this period and seems to have a relatively low rate of monumental inscription). Unlike Egypt, the conditions have never been especially favourable for their preservation. These letters depict the sort of early limes community you might expect: the bored and lonely wife of the commander, who cannot necessarily socialise with local or lower-status women but who is extremely excited to invite a peer to her birthday party, or someone promising to send a soldier new socks, or even a polite request for clarification of orders and more beer for a garrison, who have drunk all of theirs. Obviously, this is all relevant for the Romans, not the Britons, and it is also likely to have changed over time as the makeup and nature of the army did.
Vici would probably have had soldier's families in them; although officially barred from marriage for most of the period, it's likely that unofficial or locally-recognised but not imperially-recognised marriages thrived - there's a letter to a prefect in Egypt written by Hadrian that gives some inheritance rights to soldier's illegitimate children, albeit after exhausting other claims like their father's brother's, suggesting that it was a major problem. The eventual disappearance or abandonment of the vici is likely connected to the switch from soldiers being expected to pay for many provisions out of their own salary to food and other goods being centrally supplied, and it's a matter of debate where those people went - did they move inside the forts, which might have had fewer soldiers? Or did they leave for the still-extant towns? Unfortunately there are no clear answers (but a lot of arguments about gendered artefacts), much like the rest of late Roman Britain.
Otherwise, all we have is archaeological evidence, which is notoriously difficult to interpret specifics of lived experience from. What the brittunculi (e.g. the horrible little Britons, as they are referred to in one letter from Vindolanda) were up to or thought is extremely difficult to parse, although that roundhouse style constructions (i.e. unromanised buildings) appear to continue to be built throughout the period is suggestive that even if urban life is or becomes "Romanised" the countryside may carry on pretty much as before. Certainly in terms of vici on the wall, there's some significant evidence that some strange things were occurring - there are at least three probable murder victims who've been concealed within the settlement/fort (one at Vindolanda, two at Housesteads), some dies for faking coins, etc. but this is a problem of interpretation - it is easy to make some assumptions that this suggests a high crime rate, but we just don't have the evidence to make that wide a claim.
I hope that answered some of your questions!
It very much depended where you were, which frontier you were trying to cross, and when. It's important to realise that the Roman Empire never had a 'grand strategy' or a coherent, long-term, centralised plan for how the empire was going to 'work', particularly in terms of military and defensive strategy. Edward Luttwak pushed this idea in his 1976 book, which has been hugely influential but largely, among ancient historians, because showing why it's wrong is the first step in understanding anything about Roman frontiers.^(1) CR Whittaker engages with it at length and does a great job of showing its limitations - that the technological and institutional apparatus simply wasn't there for emperors to mastermind a 'grand strategy' in the very Cold War manner that Luttwak envisages.^(2) Instead, frontier policy was piecemeal, ad hoc, and usually made by the men on the spot when a crisis demanded. These men may have acted out of a generally shared ideology and set of principles, but they didn't have any overarching strategy and certainly didn't coordinate with each other.
In an earlier answer, I looked at Hadrian's Wall and what the thousands of soldiers deployed on the north British border actually did - their primary role seems to have been to control brigandage, as well as monitoring the locals - periodically conducting assessments, for instance, of tribal manpower and therefore obligations on both sides of the border (always a pretty fuzzy and uncertain concept), and training locally-raised contingents of soldiers. This probably also included collecting taxes and reacting aggressively to any perceived invasion or uprising, though it's notable that practically none of those happened throughout the period - to steal a phrase that's often used in another context, the Romans never really had a Caledonian problem, but many of the Caledonians often had a serious Roman problem. By including Hadrian's Wall, I don't mean to suggest that it was a 'typical' or prototypical frontier, but I do want to draw attention to the range of what we might think of as 'non-military' duties that took up most of soldiers' time, even on one of Rome's most heavily militarised frontiers.
The frontier in North Africa is comparatively understudied - there is however a 1998 monograph by David Cherry, which claimed that there had been no full-scale study of the subject for seventy years, and a lot of recent work by David Mattingly.^(3) The two fit together well - Cherry's expertise centres on Algeria, while Mattingly has done most of his work on what is now Libya. Both take a broadly similar view - indeed, Mattingly has a rather scathing review of Cherry's book which basically complains that it's mostly fair enough but that he's said it better before.^(4)
The first thing to understand is that, unlike some of the frontier provinces (particularly along the Rhine and Danube), most of Roman North Africa was only very lightly Romanised. That is, people generally kept the cultural practices that they had before the Romans arrived, and there seems to have been little intermarriage or general mixing between Romans and the native population.^(5) There was therefore a strong and sharp division between 'Romans' and 'natives', not only in how they identified themselves (which was always pretty flexible anyway, and Mattingly is good here on the topic of 'discrepant identities') but in how they lived and behaved. Cherry cites Brent Shaw (a major scholar of North Africa in the later Roman period, particularly on religious divisions) as as coining the phrase 'terrible estrangement' to describe Roman-native relations, but I can't find any record that he's ever put it into print.
Both Cherry and Mattingly are primarily concerned with social relations - neither writes much about what the army actually did, because the sources aren't really there to answer that question directly. We know that the army was there in force: recent fieldwork through the UNESCO Libyan Valleys Survey, has shown an intensive system of major and minor forts, supported by structures known as clausurae and what are known as gsur - fortified buildings with agricultural uses, which may have functioned as small military outposts, protected civilian buildings that could be used with the assistance of and to support the regular military, or some mixture of the two.^(6) The clausurae are fortifications that tend to block off likely routes of approach, such as wadis, with watchtowers, gatehouses and facilities for small garrisons - similar in idea to the milecastles along Hadrian's Wall.
The general consensus is that these were used to monitor traffic, particularly the movements of the nomadic pastoralists that lived in and beyond the region, and to control where it could pass. Mattingly notes that (much like Hadrian's Wall) they tend to be of pretty limited defensive value, but do tend to mark the line between pre-desert lands suitable only for pastoralism and more productive territory suitable for agriculture. He suggests that the seasonal migrations of pastoralists across these lines were a likely cause of unrest between them and more settled groups, and that the clausurae functioned as a 'labour-saving device' in defining the boundaries of grazing lands and water rights, monitoring their movement and assessing the size of the flocks they were moving, which would determine their liability for tax.^(7) The point of a clausura wasn't to stop these migrations - which would have been impossible and extremely ill-advised - but controlling and restricting them made the army's job much easier - Mattingly points to the clausura in the Tebega Corridor, which funnelled a 17-km-wide route through a single gatehouse. Seasonal workers would also have moved between these climactic zones, and there is some epigraphic evidence for Roman soldiers using the clausurae to check their credentials.
It's important that the clausurae do not necessarily follow the boundary of Roman authority - which was always a pretty theoretical concept anyway, and official Roman ideology didn't acknowledge that it even existed. There are also parts of the frontier where there isn't a sharp transition between agricultural and pastoral farming, and here there are no clausurae - the economic and social forces that gave rise to them didn't exist here.
So, to sum up - as a tribesman crossing into Roman territory from the south, your immediate observations was likely to be... precisely nothing. Depending on where you were, that 'nothing' might have carried on until you reached civilian settlement, or you might have come up to a military position where you would, almost certainly, be asked who you were, where you were going and why, and potentially charged for going about your business. Of course, being military positions, they were able to defend themselves from a very modest armed attack, but this was very much secondary to their primary purpose and neither they nor you would be expecting a fight by default.
EDIT: Corrected a malapropism - the contradictory and multivalent identities adopted by people under colonialism are known as 'discrepant', not 'discordant'.
Notes and Sources
^(1) Edward Luttwak (1976) The Grand Strategy of the Roman Empire from the First Century AD to the Third . I'd argue that Luttwak's book is much more interesting and useful as a document of Cold War political and military theory, but that's another thread and not one I'm really qualified for.
^(2) CR Whittaker (1997) Frontiers of the Roman Empire: A Social and Economic Study.
^(3) David Cherry (1998) Frontier and Society in Roman North Africa.
^(4) Entitled 'Whose Roman Africa?' and published in the Classical Review in 2000.
^(5) For more on this, see Mattingly's 1987 article 'Libya and the Limes: Culture and Society in Roman Tripolitania', Antiquités africaines 23,. pp71- 94, and the many developments of the same theme he's done in recent work - like, for instance, his 2013 Jerome lectures.
^(6) Older work by RG Goodchild and John Ward Perkins (Goodchild, R. G., and J.B. Ward Perkins. "The Limes Tripolitanvs in the Light of Recent Discoveries." The Journal of Roman Studies 39 (1949): pp81-95) saw them as 'official' military outposts akin to small forts; Mattingly pushes the other extreme that most, but not all, were fundamentally civilian buildings (in his 1994 book Tripolitania). Most treatments fall somewhere in the middle.
^(7) In Tripolitana, pp191-192.