1) cancel Available cash after bids
I get your point, but even though this would be a good idea for the BBB and tournament finals, I think in general it is bad. I.e. for most occasions and teams it is a bad idea and therefore it should be avoided.
2) don't allow to play player without paying him a salary
I'm completely with you on this one.
3) make deadline for B3 registation
Of course, and the same principle should go for the tournament too. However, no registration procedure should be needed. The only thing would be that a player needs to be in the roster e.g. at least 5 weeks before the semi finals (this is a quite common rule in most real life tournaments).
4) involve adaptability to game
Also agreed, even though I think your levels are too tough (but that's just a detail). I also think that with only one new player in the starting lineup it should get quicker to adjust than with several new players in the lineup.
3) in itself should solve the BBB issue, but I'm still for 2) and 4) also as I think they are logical to introduce.