I think what you have described is a rental activity. You cannot say that the payments you receive from the tenets is cost sharing. You take a fixed amount for rent and then share other expenses, correct? You need to include in income the fixed amount for sure. If the IRS audited and saw payments coming into your account from tenets they would call this rent.
As for the percentage of common area expenses the IRS likes to see a reasonable allocation between personal use and the rental activity. Let's say that the rented area is 20% of the house, your private area is 20% and then the common/shared area is the remaining 60%. You could say that 50% (20% rented plus half of the 60% shared) is for the rental activity.
