Given the generalities of your questions, I would answer in a general sense to your questions:
1. If the temps. where you are located are in the 40 to 50 degrees range at night you will use about 7 gallons of propane every 10 days. More if the temp is lower. Buy a good electrical floor heater from Wall Mart to help save on propane. Get a $50 to $70 dollar heater not a little cheap $29.00 heater. You want the heater to at least heat up your whole front room so you are comfortable without wearing a snow suit:)
2. Black water - if two people are normally showering daily you will fill your tanks with in 8 days to be on the safe side. If you both do a "navy shower" then figure 10 to 12 days assuming you have at least 50 to 60 gallon tanks.
3. My first choice is to always stay in Rv parks that have full hook ups or at least a dump station within the park.
4. Illinois would not be my first choice to RV at in the winter. I would do Ariz. in the winter and then Illionis in the summer.