The singular of plebs is plebs. The plural, which doesn't really exist, is plebes. It's a collective noun. One who is a part of the plebs is a plebeian.

maybe a poorer equite

That doesn't really make sense. In the Republic, the equites were not a clearly defined order, being effectively all those non-senators who had the means to run for the quaestorship. While the lowest centuries of the first voting class were probably somewhere around the HS 40k-50k mark on Lily Ross Taylor's generally accepted estimate (although Nicolet makes the unlikely proposal that this should be lowered to HS 25k), the people called equites would have been firmly within the sex suffragia. Under Augustus the equites became a firmly defined order with an established wealth qualification of HS 100k. While it was possible for a senator to be surprisingly poor, since there was no formal wealth qualification (though there was for magistracies), since most senators' wealth was in land, which is not terribly liquid, and since the lack of liquid assets tended to cause senators to borrow large amounts of cash, it is unlikely in the extreme that equites, who were freed of the rather unusual social constraints placed on senators, should have the same problem of debt.

You would think there would be a disproportionate amount of women after the Marian reforms

No you wouldn't. There is no evidence for a reorganization of recruitment in the first century. And even if we want there to be one, the effect on the urban population would have been negligible. Brunt showed back in the 1960s not only that the Romans continued to favor rural recruitment (we had known that already) and target pretty much exclusively the countryside in conscription, which never ended during classical antiquity and was not ended in Italy until Tiberius, but that rural recruits and conscripts almost entirely dominated the armies of the first century and the early Principate, after which point recruitment passed more or less exclusively to the provinces, with Italian recruits making up less than 1% of all military personnel by Trajan. Urban recruitment was quite rare, restricted almost exclusively for manpower crises, as during the Jugurthine War and again by Augustus when he, according to Velleius 2.111, levied the freedmen of wealthy city dwellers to form a defensive force for the city, which he at that time feared was within days of being attacked.

no organized fire brigade (until Crassus extorts your property first).

This is also mistaken, based on an incorrect reading of what Plutarch actually says. Only Plutarch reports this as well.

There's a lot of questions here. You're asking for a book or books, and there are some out there for you--a lot of Mary Beard's books, for example, might be up your alley. However, if I'm understanding you right, you're not really asking about "day-to-day" life, you're asking about the sum of the social and economic experience of living in the city. On that we're on much shakier ground. While we can point to particular objects, customs, and locations--say a public latrine--and say aha here's an element of common urban life. But we cannot get into the heads of most people, and we cannot motivate them, and we cannot construct schedules or daily plans for them. For that we would need textual evidence of very particular kinds, and by and large we simply do not have it.

A few things nonetheless might be said. To begin with the very phrasing of your question, we do not really know whether Rome had anything we could realistically call "slums." I've written in this direction before, although more often people are interested in ethnic districts. There's great uncertainty as to how wealth in the city was distributed around its residences. There is no doubt that the majority of the urban population lived in insulae, but first we don't really know what a typical insula at Rome actually looked like at any given period. We know, for example, that Nero's building regulations were generally ignored at Rome, probably because it would have involved significant inconvenience. At places like Ostia there are insulae with large colonnades and impressive stucco, but Ostia is an unusual city, significantly rebuilt over the years and preserved for us in its fourth century state. Similarly, Pompeii's insulae are probably not typical. More significant, both Ostia and Pompeii show domus and urban villas mingled in among insulae, often with little in the way of settlement patterns. This, along with the fact that areas like the Subura and the Aventine had expensive domus mixed up among the insulae, has caused some (e.g. Lisa Mignonne) to speculate that the basic unit of architectural social structure was the domus, around which insulae might cluster. I am highly skeptical of this suggestion, for which there is very little evidence, but there is certainly abundant evidence that wealthy homes, with the exception maybe of horti, could be found as easily in places like the Palatine as in places like the the Subura. And there's that weird tradition that I still have to work out in my research of thinking of domus as if they were fortified centers of activity within the city, as described by Cicero in the Pro Milone and before the death of C. Gracchus.

To quote Fagan, "the public places of ancient Rome were not particularly safe." But this applied to the elite as much as to the common man. Indeed, our evidence mostly comes from senators being attacked and beaten in the streets, the baths, and not infrequently their own homes. We know that the city must have been dangerous, particularly at night, for the common man, but we really can't reconstruct that experience. Clearly people were not being beaten up left and right in the streets in broad daylight--lack of police force aside, Rome was clearly not an anarchy. Yet vis was an accusation reserved almost entirely for the elite, since it was considered a capital crime. Yet we know that, for example, civil suits for furtum, theft (considered a civil offense in Roman law), occurred quite frequently. Furtum was a relatively broad crime that included fraud, but many of the cases that we know of from the jurists are in fact theft, sometimes complete with violence. Moreover, the distinction in the Empire between honestiores and humuliores is unclear to us.

All this is to say that, while we can identify phenomena, we cannot necessarily say very much about them. Even something like labor, for which we have a surprising amount of evidence, is a bit of a mystery. We've been pretty sure since Brunt that labor in the city was semi-migratory, and Brunt argued persuasively that suburban labor and urban labor rotated back and forth through the seasons. But nonetheless the great mysteries for us are the degree of mobility in labor and the schedules of day laborers. We know that day laborers dominated the unskilled labor pool of free workers, but we do not know how likely it was for them to find work on a particular day, how they might spend the day if otherwise unemployed, or really much else about the actual function of the unskilled labor market.

There is definitely more to to be said here, especially with some of the more specific aspects of life you're interested in, but whilst we wait for an answer, you might find some of the answers in our FAQ on Daily Life in Ancient Rome an interesting starting point.