"File together"? You can't file a combined return with another person unless they are your spouse. You report your own income and deductions on your own return.
Address--the address on your tax return is where you want to get official mail from the IRS. Unless you have a post office box I suggest you use your current mailing address even if it is your sister's house. The IRS won't be sharing that info with your sister's mortgage bank.
Your sister doesn't have to report the rent as income. Family can live together and share expenses without making it rent. But if she does not charge rent then she can't deduct expenses. And if she doesn't charge rent then you can't claim any state renter's credits if your state has such a thing. On the other hand, if she does charge rent so that she can deduct expenses, she has to charge a full fair market value rent, or else she can only deduct expenses equal to the rent, she can't show a loss and use it against her other income. But that's more her problem than yours.
