I am trying to edit a player, but their ratings, and talent level (1 star, 2 star etc) is not showing on the main menu screen. Also, if I go into the database and change the team name of someone, it does not remove them from the team. Am I doing something wrong, or is it like a bug or something?

Not real clear on "is not showing on the Main Menu Screen", but if you edit a player ratings they do not change right away on the roster screen. You will have to wait until the team is re-scouted before the coaches rating update as they do not know they changed.
You cannot move a player from one team to another from an export due to players ID numbers which you do not see in the editor. The only way is to edit and existing player to the same name and ratings, then change those things you just entered on the original player. You will lose his history though.