1) If you raise the min from $0 to $4, then $4 becomes the new $0. $0 should be the min for any budget. The impact of that could be different than it is now. Like 0 for all projections, if you want to go extreme. Which is what you seem to be proposing in (2). The root problem is the entire ADV is poorly designed or programmed. That and that players all pretty much develop the same way. Fixing that would probably accomplish what you're proposing.
3) It's not easy to get someone to take over a team that's been badly run for several seasons. If that team gets one or more busts for their top draft picks, it will be even harder to find someone to take that team. There would be consequences of what you're suggesting. There's a chance you're not thinking them all the way through. You can't just think of the ideal team where the same owner does a pretty good job at the game for several seasons. The game should allow worlds to go on even if they have a few really bad or negligent players for a few seasons.
4) I agree that some mid-round draft picks should make the ML and some should be all-stars, but it should be rare and based on merit, not luck. If everyone gets a DITR, then they really don't help anyone. I'd like to see DITR correspond to a combination of MinL W/L record, coaching, and playing time. Seems to be random now. And they are only RPs, Cs, and crap infielders.
5) I think you are 100% right on this one. It's silly that we can't overbid our total FA budget. Completely unrealistic. There are dozens of ways to change the game logic that would allow that without destroying the FA process. This has been suggested before. If you continue with this, you're going to see that a lot of the guys that bother to post opinions here don't understand that changing this would be good for the FA process. They can't see past the current logic.