I had to give up on the third level as the controls just don't really work well right now.
The fact that A and D turn instead of strafe could work, but the fact that the camera is not locked directly behind the player, and that turning is so sensitive, makes movement really weird and jarring. I get what you were going for with the frog (I think), but the fact that the frog can't even turn makes it a lot harder to actually use.
Furthermore, the jump strength is an interesting idea, but I don't feel it works, at least not with the way you have the levels set up. I felt like the jumps in the third level were way too tight, and with the way the frog works, it was almost impossible.
I did manage to try out the plane. I thought it was a bit strange that I had to be in the air to fly, but I can understand the reasoning behind it, I'm not sure it's very practical though. Additionally, the turning on the plane was extremely slow, which I found strange because how sensitive the turning was on everything else.
One more minor issue I had was the way that you unlocked new shapes, with a menu just suddenly filling the whole screen just by touching the chest. It felt very jarring. If the player had to interact with the chest or if the menu didn't fill the whole screen it might feel better.
I wish I had more positive to say about the game, but the current controls really take a lot away currently.