He's fine as long as he is just walking up the stairs. You don't want him trying to sprint up and down as quickly as possible. That is where his feet could get away from him he could hurt himself.
Dogs that get hip dysplasia primarily end up with it because they are genetically predisposed to it, not because they climbed some stairs when they were younger. With all the worry about all the little things people think can kill their puppy, it's amazing how resilient young pups really are.
For joint support when feeding raw, any part rich in connective tissue is good. I know you're just starting out, so it will be pretty much chicken feet. I throw in a foot or two every couple of days. When you start adding more proteins to his diet, things like cow and pig noses and tracheas will also be good.
He'll be fine at the dog park. It's just fine for puppies to run and rough house. The important thing is he can stop and rest if he needs to. Exercise trouble happens with puppies when someone forces them to do intense exercise for long periods of time such as someone taking him for a continuous three mile run.
Mine actually had some pretty steep stairs to go up and down in and out of my house. He climbed them from 10 weeks to a year and now I'm in an apartment where he climbs 15 up and down several times a day for walks, potty breaks, trips, etc and is fine.