Sorry, it's been a while since I played the predecessors, so I couldn't remember how dives worked with momentum. I think my main issue with it is that you have to wait before you can proceed with normal walking or a jump. I'm maybe being too picky about that.
I see why you would want to distinguish the charge from a normal run, and I think it should work. The thing I'm most concerned about with it is that you're not able to start charging while already walking. I feel like having to trigger it while standing still is unnecessary. Not being able to stop the charge instantaneously makes sense, though. I will say that the somersault is a pretty nice touch/reference. If you wanted to implement a charge jump to dive chain, you could limit spamming by only allowing the dive to happen once at the apex of the somersault. I didn't think of diving into a charge, but that could certainly be cool. That said, I'm not much of a game designer. I also noticed that you no longer gain height with the dive, which seems like a good change.
With the backfilip, I think the issue I have is that I press the direction and then immediately follow with the jump button instead of waiting for the direction change animation. I may just be too hasty about it.
I also kind of like the wicked damage boost jump. It's very difficult to pull off, so I don't think it should wreck the game.
While the game seemed to have low FPS, it didn't affect play very much. Probably just made things a bit more floaty, but it would certainly look better without the drops. The horizontal scrolling was not very smooth for me.