What you suggest does little but not much more (it's not nothing because you give an option to return to school)to fix the single biggest problem with college basketball, the lack of skilled talent.
The only way that could ever be fixed would be to force the talented players to stay 3+ years. Only the NBA could do that, but they won't because it's not in their best interest, and it would be a publicity nightmare.
6 fouls over the course of 40 min when the NBA does it over 48? How does that make sense? You want unskilled physical teams to have an advantage? You actually want the game uglier?
Your cheating suggestions sound great until you have to get into specifics. What defines cheating? Is every violation exactly the same? Do you punish an isolated minor violation the same as a major repeated one? People complain about how large and specific the NCAA rulebook is, but the people to blame are the coaches, boosters, ADs, and players. Anytime you have a rule that isn't specifically defined, someone will find a loophole to take advantage of the people trying to live by the intent of the rule. Can you rewrite the book so that it is fair and loophole free?
No investigation over 1 year? Ok, so if you're good at hiding stuff you just have to hold them off for a year. Well that certainly gives the NCAA the teeth to do all of the banning you suggested.