The senate of the late republic and early empire isn't really difficult, once you get used to looking at it as its own thing, and not some kind of elected legislative body that we're used to from the US senate.

Traditionally, the senate was a panel of former magistrates that advised the current magistrates. Former tribunes of the Plebs, although not being magistrates strictly speaking, are included by the middle republic in this body. Basically it's anyone who has won election to at least quaestor.

While generally being a senator (more of a status than a job) was a lifetime thing, there were a few restrictions. A senator could be removed by a censor for immorality (however defined), perhaps for insufficient wealth (wealth restrictions change over time).

By 267, eight quaestors (the lowest qualifying magistracy) were elected each year, and that increased over time until under Sulla Rome had 20. So that's somewhere between 10 and 20 new senators per year, and that kept the senate somewhere around 300 by senators dying by old age or war, or retiring, or committing sufficient immorality for removal.

Sulla changed the nature of the senate drastically. In addition to raising the number of quaestors 20 (possibly from 19 already), he just picked 300 people to be senators without election. In part, this gave him a significant number of clients in the senate, but he also made the senate the jurors of court cases. In fact, jury duty might have become the primary responsibility for senators at this point. He needed 600 jurors to staff the courts.

Caesar doubled the number of quaestors to 40. 40 new senators a year! So the number of senators over the next decade rose to 900, which Augustus reduced over three different revisions of the senate (senators in total, and number of quaestors elected). Augustus wanted to manage government through legates and not through elected magistrates.

Augustus' restructuring of the senate included an increased property qualification to a million sesterces, which distinguished the senatorial class from the equestrian class, though election to quaestor was still needed to qualify.

I'm curious about what you've been using for your research. I used the entries on quaestor and senate in the OCD for my dates and numbers. I would also suggest Lintott's book The Constitution of the Roman Republic. Flower's Roman Republics has a good chapter on the Sullan reforms of the senate, and explains some of the effects of his changes. The OCD cites, in addition, Syme The Roman Revolution, Talbert, The Senate of Imperial Rome, probably most useful, and other books as well.

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I think that the primary reason you are confused is that the Roman Senate existed for over 1000 years, and unsurprisingly it varied quite a bit during that period of time.

It's kinda like asking "Historically what are the main responsibilities of the Mayor of London and how were they selected", it wouldn't be surprising that Boris Johnson focused a lot more on subways and television advertising to win large-scale elections for example than Henry fitz Ailwin did when he held the equivalent role 800+ years ago. Now consider that the length of time between Henry fitz Ailwin and today is several hundred years less than the duration of the Roman Senate.

For about half of the duration of the Roman Senate, there was no Roman Emperor at all (this was the period of the Roman Republic), and then for another approx 100 years at the end there was a Roman Emperor in Constantinople who either didn't care about or had no relationship with the (relatively useless and powerless outside of the local area) Roman Senate.

Maybe do another post about the specific time period that you are thinking about and people will be able to give you better guidance, but honestly it sounds like you have a lot more to learn before starting a fantasy novel based on the Roman Empire.