These questions are way too vague for me to want to answer them.
Nothing vague about them. OP is speaking in generalities, not specifics and understands that answers will vary. Obviously he's trying to extrapolate data to use for his own baseline perhaps on where to start looking.
1. As most have stated, it depends on your unit, how much cooking, heating, etc. Using my Endura as an example, we had one very large propane tank. Can't remember how big and can't seem to find the spec, but we camped from spring to fall and filled up once to twice a season, depending on weather.
2. We'd shower as often as we wanted to. We left gray tank valve open as we always used FHU site. Black tank would stay closed and would last 3-4 days, depending on how much we were actually in the campground. This will vary greatly depending on how many people, adults vs. kids, etc. Never boondocked so I can't give that comparison.
3. If you have a 4-season unit, then yes, you can probably us it year-round in Illinois assuming you can find dump stations and a place to park it.