1) The mind-contoller issue was addressed in his introduction. Also, the school requires both good grades and useful skills.
2) Because he has years of internalized inferiority issues that he hasn't shown sufficient progress in. At no point does he walk away from an undignified situation. The option to walk away when you're not being respected is one of the most important things in maintaining one's self-respect, and Deku's refusal to do this (particularly with Bakugo) makes him look like a battered wife.
3) It's implied that most professional heroes have, in fact, done more than the students have as part of their careers. The students have resolved less than a dozen incidents, although Protagonist Incident Magnetism is definitely in full effect.
Furthermore, the setting is one in which superheroes are heavily regulated by the government.
4) Welcome to the world of jobbing. While 7/5 INT-chan was a filler character, the characters that do appear in the manga don't always use their powers in the ways you might expect them to based on how they're introduced. Horikoshi isn't that great at writing strategy, so characters like Momo and Shoto will underutilize their powers, while characters like Mineta and Bakugo will push the limits of plausibility with their superpowers.