Thanks! The controller support is wonky currently because I don't actually have a controller to test it on, so I'm implementing it blindly. Controllers not working for menus is a known bug, which will be fixed for the final game. I really thought I implemented a dead zone and was told when I was having someone test it that it was working, but I'll look into fixing it or making it better. I'm not really getting what you mean with the sound. I went to test it in game and the sound plays exactly when you press the jump button, and the code for the sound reflects that. It's possible that you're getting some weird GameMaker sound lag, but I don't know if that even exists or not. I'll ask some other people on other computers if they notice it, and I'll see what I can do.
And yeah, we haven't implemented death or checkpoints yet, but I figured it would be fine to just let the game play out like this so people would be able to explore without the annoyance of dying. Options and key-rebindings are planned!