How old is the new cat? Sounds like a young one... Is he neutered? I assume the older cat is.
When you bring a new cat home, it's only natural to have some hissing and growling. Cats are territorial and feel intimidated when they meet new cats. Usually, with time and patience they become used to each other.
You should introduce them gradually and let them get to know each other in stages. Eventually, some social hierarchy is bound to form - that's the way cats are. Very possibly, the new cat may become the dominant, but thatâ€™s okay. You should let them sort out the hierarchy by themselves.
Never shout at them when they're together and definitely never punish them. Try to make them associate each other with positive things. Play with them and pet them a lot when they're together and give them a treat.
As for the younger cat biting you - this could be related to his young age. Kittens love to play roughly with each other and may try to do the same when they play with us. In a couple of days, I'll publish an article in this site about cat aggression. Maybe you could use some of the tips and techniques.
I'll post here when it's online. Of course, the best way to know about any new articles is to join the newsletter mailing list by sending an email to:email@example.com
I'm so glad you took a stray cat into your home - they need love and care too!