I fill the propane (top it off, at least) at least once every two years. But one time when traveling during winter in Texas, I was having to buy more LPG, about 6-8 gallons, every 2-3 days.
I can use my shower as often as I want to. When the waste tanks fill up, I dump them. Sometimes I have a sewer hookup at my parking site, more often I've had to unhook and drive to the dump station. There is also the option of dumping into a portable waste tank (often called a Tote, that is one brand) and hauling that to a dump station.
Two people might fill my black waste tank in 3-4 days, six people might fill it in one day. My gray tank will fill with 4-5 showers, combined with a couple days washing dishes. But this depends on patterns of use and waste tank size, there are tanks smaller than mine, and tanks much bigger than mine.
You can live in a RV in Illinois, but in the winter you might be cold no matter how much LPG you burn in the furnace, and you might have to be creative about getting a water supply and keeping it from freezing. Not all RVs are the same, some are much more usable in winter than others. The great majority of what is sold is designed for two or three season living, and that is to keep weight down for mobility, and keep costs down to meet low price points. But there are RVs that are as livable as mobile homes.
The issue with winter in Illinois will be where to live in it. Not all RV parks provide full utility services in the winter, many are not even open. But people do live in RVs in the far North, converted for winter use on a permanent site, i.e. the RV becomes a smaller equivalent of a mobile home, no longer moves like a RV.
You will find dump stations at RV parks, some travel centers, and at public campgrounds intended for RV use. Some states have dump stations at rest areas, haven't paid attention to that in Illinois, but I think I've seen this at least at one rest area on I-57 between US-24 and Urbana.
Not all dump stations will be open in winter.
If you are thinking about buying some kind of RV, parking it in a driveway somewhere to use as a permanent home, then you need to be thinking about converting the RV into a small permanent home. That's not really difficult to do, but you need the kind of winter-protected utility hookups found at mobile home parks, not RV parks. And once converted to use these, the RV becomes less useful as a RV.