correct me if I'm wrong since I'm in no way an expert but I believe that black widows education came from the black widow program which I guess in some ways was an assassin school.
Team Cap all the way! In a way this is basically the same as registering a certain group (based on race and what not) because a group within them commit heinous crimes
In the movie: The Avengers are considered a private group, but because of the collateral damages and death they sometimes cause, the world leaders went them under control of the UN (or something along those lines). Team Ironman is for it, team Captain America is against it. That's pretty much the gist of it.
I AM ON TEAM LETS GET OUR SHIT TOGETHER AND HAVE A HAPPY ENDING PLS