Rescued a cat and I guess he’s mine now?

Sooo… a couple of weeks ago a cat literally walked into my home. He has been so nice and calm to the point I am 100% sure he was a pet at some point. We took him to the vet and there was a microchip but no information so we posted a few places but have heard nothing back. I was going to give it another week or two and then was planning on claiming him myself and taking him to the vet for shots.

As he has gotten more comfortable, he has become more energetic and explores more. This is my first experience with cats and I am very timid around them. Today, he was in my lap and he bit me… hard. He was sitting there purring and I was petting him. After he bit me he didn’t leave my lap, just readjusted. Why did he bite me? I just need advice and support. How do I discourage that behavior? He always seems hungry, how much do I feed him? He has some toys and a litter box and food and water but is there anything else I need to do?