[Try not being a villain and maybe they'll invite you. Face turns are totally a thing.]

No, the Justice League is all different people. Superman and Green Lantern and Aquaman and-- [those are the only ones she knows, oops] --some others.

The Avengers do aliens and supervillains. They usually don't handle crime unless it's seriously large-scale. Day-to-day stuff like that is more Spider-Man and Daredevil's thing.