2)bearing a gun in public is called "open carry" , it is legal in my home state of oregon, i open carry anywhere i go, to the market, to the movies, to the library.... my gun on my hip.... in some states open carry is not legal. again, a patchwork of laws.
3)yes, people on vacation are allowed to shoot IF they are legally able to possess a firearm here in america... again all states vary, a patchwork of laws. BUT you are legal entitled to do as a normal citizen would do, while on vacation. in most places.
there are many forums about handgun laws and open carry ..... handgunlaws.us and opencarry.org will give you statutes in each state.