In the USAG women's program, you can only specialize as a Level 10 and still qualify to states, regionals, ext. However, I have known level 8 and 9 gymnasts who, for one reason or another, decided to only compete certain events. They couldn't qualify to state meets or any meets past that because of their low all around scores, although they were able to compete their chosen event(s).
As for the starting level of competition, that depends on your state and your gym. In Florida, most meets include levels 2 and 3, and there is a level 2 and 3 state meet. However, I'd say most people don't start competing until level 4 (or even 5).
it depends. some gyms will let you compete only certain events... but you cant qualify for states. you can also start competing in level 4 (mostly) but some gyms dont compete level 4, they just go straight to 5 (like i did).