Aggressive cat behavior?

I have a female cat 2 years old, and a male cat 6 months. I just got the male neutered last week and since then everytime i open the door he runs outside and i have to chase him to catch him and get him back in the house. and our female cat sometimes will be sitting on your lap and randomly just bite you. Not hard but its still annoying. You are holding her & petting her and she just bites for no reason.