Yeah you're pretty off the mark. I'm not sure what's given you the impression that proconsuls are effectively the same as former consuls, but they're not. A former consul is a consular, and is simply a highly influential member of the senate, such that the consulars speak first in senatorial meetings (after the presiding consul introduces the matter at hand and the consuls-elect speak). A proconsul is simply a magistrate--not a senator--invested with consular imperium, meaning that he can outrank other commanders and is able to call on more military resources and manpower more easily. In practice this means that he's not a former consul, but rather a consul whose office has been extended.

What I think you're probably observing, although honestly it's a little difficult for me to tell from the way you've described your issue, is the prorogation of magistracies. Starting already in the third century and continuing effectively until the end of the Republican period (and through to the imperial period, technically), commanders in the field often had their imperium prorogated, which is to say extended past their formal year in office. Officials could have their command prorogated either by a vote of the people or by the senate, and Corey Brennan has suggested that there was a technical division between these two things. Either way, usually a commander's imperium was prorogated because his theater of war (i.e. his province, which does not mean an administrative territory until well into the imperial period) was still active and sending a relief force was premature. Prorogated magistracies are basically the same thing as the parent magistracy, since it's literally just an extension of the command. Theoretically they no longer carry a civic function, since those functions are now being exercised by the new magistrates at Rome, but in all other respects prorogated magistrates behaved exactly the same as they had during their formal year, and were treated the same way (e.g. they weren't supposed to be brought to court unless they were recalled from the field). In any case it's a little bit of an artificial distinction, since the highest magistrates--the consuls and the praetors--were basically military commanders first and civic magistrates second, with the exception of the urban and peregrine praetors who typically remained in the city except in emergency. With the consuls in particular this is especially true, since before the 70s consuls only remained in Rome for typically three months, leaving for their theaters as soon as they had overseen the elections of their successors. Indeed, it's not so much that a proconsul or a propraetor had his imperium prorogated in a particular area (his theater) and not in the city, it's simply that once military command was taken up outside the city it couldn't be brought back into the city, meaning simultaneously that one would be forced to renounce imperium and that imperium, if renewed for an individual outside the city, only applied to imperium outside the city. This I suspect is one reason why you're having difficulty with Livy, etc., because the terms proconsul and propraetor aren't Latin words. A magistrate whose command was prorogated was simply considered to be exercising the same office for an extended period, and did not receive any kind of special title. Basically the only time when we find the term "pro consule" is when a praetor in the field has been granted an extension to his command in line with the authority exercised by a consular commander. For consuls whose command had simply been prorogated there's no special term, and both the Romans and modern historians simply continue to refer to such commanders as magistrates, because that's what they are.

Since the most critical theaters tended to be assigned to the consuls, consuls were often prorogated and assigned to remain in the field for another few years until the campaign was concluded. However, consuls weren't the only ones prorogated. Praetors very frequently were as well, and statistically I think they're much more common, although I'd have to check Broughton and Brennan to make absolutely sure. Additionally, propraetors are effectively the only kind of imperium-wielding "promagistrate," if we use the (not real) word strictly to mean individuals not holding a magistracy with imperium who have been granted imperium, rather than prorogated magistrates. For example, when Antony was granted military authority in Italy early in the civil war, despite being only a tribune, he was acting as a tribune with imperium pro praetore. Similarly, the young future emperor Augustus initially received military authority pro praetore without holding or having held a magistracy. Cases like the former are much more common than the latter, although both are quite rare. When individuals were invested with imperium higher than their actual rank they almost never exercised it as private citizens. Rather, existing magistrates were much more typically given an extension of their commands. Also relatively common (but still unusual) were the delegations of command by a (consular) commander to legates, who could be invested temporarily with imperium pro praetore. Both Caesar and Pompey used this expedient to be able to conduct campaigns on multiple fronts. By contrast, the only examples that I'm aware of of individuals being given imperium pro consule are praetors whose commands have been expanded--again, prorogated consuls aren't really acting pro consule...because they are consuls.

Quaestors can be prorogated too. Since most quaestors were attached to the command of a consul or a praetor in the field, if their commanders' commands were prorogated theirs typically were as well. Quaestors aren't terribly important, and they rarely appear in the narrative sources, but there are a couple of pretty well known examples that might not be immediately obvious as prorogations. When C. Gracchus was serving as quaestor in Sardinia his magistracy was extended for a second year, i.e. it was prorogated. Occasionally you can also have quaestors temporarily granted imperium pro praetore to act independently overseas when no one else is available. As aediles are entirely an urban magistracy, it doesn't make sense to prorogate them (and it can't really be done). Moreover, unlike the quaestors, the aediles don't leave Rome, meaning that prorogation would be about as procedurally possible as prorogating the tribunate. Nor would you get someone appointed "pro aedile" if, say, one of the aediles died or somehow lost his office. First of all, the aediles don't have any imperium, so it doesn't make sense to make someone act "pro aedile." Second, if officials in the city die or somehow lose their magistracy or are unable to carry it out (e.g. when Nepos fled the city as tribune in 62) usually they just don't get replaced, unless it's a consul in which case a suffect consul is elected--note, elected. Elected magistracies within the city are supposed to stay elected, whereas a command pro praetore overseas can be the result of a law passed by the citizen assemblies, but it can also be an emergency appointment made by the senate.

And no, this doesn't really change under Sulla. If you, I don't know, look this up on Wikipedia or something you're probably going to see that Sulla required consuls and praetors to remain in the city during their years and then automatically made them promagistrates and sent them to the provinces the year after. That's not true. There's no evidence that Sulla made any changes to the way that magistrates took command over their provinces. Such changes didn't occur until the Lex Pompeia in 52. In fact, consuls and praetors after Sulla didn't actually stop taking over their assigned theaters during their year. It's just that the assignments were made late in the year, and for whatever reason during the 70s (a poorly documented decade if there ever was one) it appears to have become customary for consuls and praetors not to depart for their assignments until quite late indeed, at which point prorogation would basically be a necessity. Keep in mind that by this period a number of civic functions--in particular the elections--have been pushed back later in the year, meaning that the consuls have a reason to stick around longer. Usually consuls and praetors left for their provinces in the last days of their year--cases like Caesar, who sat around outside the city for a good couple of weeks at the beginning of 58 before heading north to the Po, were not usual. Where things changed was really in the imperial period. Since, after Augustus, the emperor was granted consular command (now no longer necessarily tied to the office of consulship thanks to the personal privilege of imperium maius extended to the person of the emperor) over all militarized provinces, anyone sent to take command in those areas was acting as an independent legate, i.e. a legate with imperium pro praetore, praetorian imperium still being the default. These men were not office holders while they were in the provinces, but they were usually of praetorian or consular rank, avoiding the possibility that a lower magistrate might have his authority expanded above his station. In the non-militarized provinces, the Republican system of appointing ordinary magistrates persisted.

This is simultaneously an easy question to answer, but also a hard one. There are a lot of technicalities I'm going to try to avoid unless forced to acknowledge by the other Romanists here.

The original conception of a Roman proconsul is someone who is delegated to have imperium prō cōnsule ("power in place of a consul"). From there we get the adjective prōcōnsulāris/e "proconsular". The Proconsuls were imagined to be extensions of the power of a consul, and they existed because the two Roman consuls could not possibly be everywhere they needed to be at once, especially as the empire grew in size, and it was too much against the mos maiorum for the Romans to contemplate expanding the number of elected consuls beyond two every year. The very earliest concepts of proconsuls were typically via prorogatio, or the extension of an extant consul's term beyond the given year. So for instance during the Second Samnite War, the consul Q. Publilius Philo had his command prolonged because it was a war emergency (Livy 8.23).

The concept did extend to praetors, and in fact originated with praetors. We often get propraetors, or, more specifically, we see men given imperium prō praetōre. Such a role was, by definition, given to men who did not hold a magistracy but were empowered to command Roman soldiers. It was a delegation of imperium. Praetors were the original governors of provincial possessions as Rome expanded, and in the earliest times were the military commanders. We see delegation of praetors' imperium very often in the Late Republic, e.g. for the legati of a Roman general (like Caesar's Labienus or Sabinus). Their imperium flowed through the Roman general, who might himself be a proconsul. There was also a steady expansion of the number of praetors per year in their capacity as judges. This is somewhat separate from the old traditional role of the praetor as a commander of soldiers. So we get both an expansion of the praetor corps as time goes on, and also the generic use of the concept of imperium prō praetōre. Praetors in general are a difficult topic, and a gigantic study has been made of them by Brennan (Praetorship in the Roman Republic 2 vols, Oxford, 2000). Your question about Sulla belongs here: there had always been an understanding that most praetors, upon election, would hold their regular imperium and do the judge thing in the Capital for one year, then go out to govern a province in their second year with prorogated imperium. By the Late Republic, it had become a de facto 2-year post. This was formalized in Sulla's lex Cornelia dē provinciīs ordinandīs, which also officially formalized the length of the proconsular and propraetorian "term" to 1 year. It empowered the Senate to "legally" administer the promagistrates without it needing to be recognized as this special dispensation every time. Instead, a promagistracy of longer than one year became the exception, not the default rule. (There is much more to Sulla's activities here regarding promagistrates, especially concerning the lex Curiata of those with imperium, but I'm not digging in to that now).

The concept extends to quaestors as well, but this was more rare and was usually the product of prorogatio. If a quaestor needed to stay on in the role, usually because of the prorogatio of the higher magistrate to whom he was attached, he became prō quaestōre. Quaestors had no imperium by default, but could of course at any time be designated legatus or be appointed to take the place of their superior with grant of imperium prō praetōre. Sometimes we do see quastōrēs prō praetōre. If a praetor or proconsul became incapacitated, a quaestor could assume his duties in a limited way and therefore received imperium via that delegation. Even if he were to take the place of an incapacitated proconsul, he still got imperium prō praetōre. Secondly, someone who was still just at the rank of quaestor could be appointed to command troops, and therefore be quaestor prō praetōre. Cato, e.g., in 58 BCE was sent to Cyprus in this capacity. This title also crops up in the Principate, especially in financial administration of the provinces.

There was no concept of prō aedile, however. I'm not sure what happened if an aedile died.

A fun fact about imperium proconsularis is that it was, in technical terms, far more sweeping than the power of consuls within the city boundaries of Rome, where precedent and rules rather strictly constrained them. In the field, a proconsul of the middle Republic enjoyed all the powers of the kings of old. Sometime after the Punic Wars, Romans were given the right of appeal (provocatio) in such scenarios (Sallust Jug. 69), but in many other ways it was pure autocratic martial law. Proconsuls were subject to audit after their term, of course, like Verres, but what they did on campaign was nigh absolute.