Question 1: I believe this is considered cost-sharing and I do not need to report anything on my tax return.
A. That is correct. There is little or no IRS audit risk, as even when these things are rent (and that's seldom), it usually results in a loss, not a taxable profit. A loss would not be deductible. That's actually the more common question, in this forum: can I deduct the loss from renting out a room in my house? The answer is no. The "personal use" rules prevents this.
Question 2: I assume now my girlfriend can no longer claim head of household?
Simple answer: Correct, she can not claim HoH. However, if she can show that her $600/Mo contribution to expenses amounts to more than half of the total household expenses, she can be HoH. Food expenses are also part of HoH qualifying expenses. The fact that she doesn't pay rent, does not exclude her from being HoH. Her contribution being only "nominal" would prevent her from claiming HoH.
