13yrs old is never too late to dance, and you won't be put in with the little girls, usually the dance school would ask how old you are and then they will put you in a class with people around the same age as you, but they might also ask you to take a few lil learner lessons for you to learn the basics steps and stuff like that :) But I would say go ahead with dance :) and youll catch up even if the others have more dance experience youll catch up to them and also it doesn't matter if your not super flexible, youll pick up flexiblity the more times youve been dancing :) Hope this helps :).
Of course not. Think about Misty Copeland. She was 13 when she started and now she's a soloist the American Ballet Theatre.
But in order to get to level you want, you'll have to work harder because you're starting a bit later.