Will living in my home affect my sister's eligibility for Medicaid?
Yes, the fact that your sister reported that she pays no rent could be a problem when Medicaid considers her eligibility. When deciding whether someone is eligible, Medicaid looks at all the person's income and assets, and also at the person's regular expenses, including rent. If the person who's applying does not pay any rent, then Medicaid considers that the income that person has can go to help pay for other things, including medical care. So, a person who pays no rent is less likely to qualify for Medicaid than someone with the same income who does pay rent.
Your sister should get in touch with the person handling her application at the local Medicaid office and make sure that the application shows that although she doesn't pay rent, she does buy the food and pay bills. If that doesn't work, you may have to change your financial arrangements with your sister. Instead of paying for all the food and all the household bills, your sister could pay you rent plus one-half the household bills. You could then turn around and use that money to buy your own food separately, and for the rest of the household expenses. In that way, your sister might be spending her money in a way that could satisfy Medicaid eligibility rules -- and be perfectly legal, since your sister isn't hiding anything or giving away her money -- but without either of you actually changing the amount of money you personally spend.
Great answer!