A he just lives here, no rent, no payment to me of any kind, no contract, would this still be considered a tenant/landlord relationship?
Yes. He's clearly getting mail there, so he's your tenant, whether you collect rent or not.

Also I'm concerned when he files his income tax, he uses my home address..is that something to be worried about?
No more so than the library should be concerned if he uses that for his mailing address.

You have no responsibility for his bills or taxes.