help me evaluate my new dog

I rescued a dog from going to the shelter in Sacramento
his name is Bubba I've had him for 2 weeks he's my first ever dog so I'm confused and need some help about some of his behaviors and if I'm doing the right things.

He's a Lab Pit Mix.

-First of all I learned that my Wife is very allergic to him so, hitch 1 he doesn't stay inside with us as originally planned. we keep him outside. I live in an apartment so the backyard is only 10 by 20 feet.

-He does play with my kids about 1 - 2 hours a day. I jog him for 15 minutes in the morning and walk him for 30 minutes in the evening.

-I thought he was skinny but I'm not sure he looks healthy except you can see his ribs a little through his skin. I'll post a picture when my camera's working.

-He seems very fearful of loud noises and sudden noises, but he's very outgoing to go up to strangers to be petted. and will play with any and all dogs. although when a fight breaks out in the dog park he runs and hides.

-He doesn't take treats like pupperoni I bought from the store. and he won't play with toys, the few that I've tried. he doesn't chase after any toys and he'll only eat dry food if its mixed with wet.

-He's never barked once which is odd. he's never showed aggression to anyone not a growl or anything even at my 3 year old who can test anyone. Ears are almost always back but tail is never tucked under unless he's really scared.

Any insight on what he needs would be greatly appreciated