I don't know about a real gun, but a bb gun can get you some food quietly......Even if you can't have a real gun with you, there are still knives and machetes that can help......

all firearms are prohibited in national parks, most state parks and most likely your city parks. this will include slingshots i think.

This would depend on where you are camping and what state you are in. In many states, having a weapon is illegal. If you have a registered weapon in a state where it is legal to keep a weapon, you would probably be legal to bring a gun with you while camping, especially when there might be someone or something that may do harm to you. This would mean that you would be using if for self-defense. There's no doubt that you can bring a airsoft with you, though. Airsofts are legal in every state as long as it was airsoft qualified, and as long as you don't go into anywhere with a large amount of people. (A town or city)

check with your local fish&game office