You managed to get a lot done, and the character has a kick ass attack animation. The jump is what needs the most amount of work, I think, considering that fine movement controls seems important to the goal of the game. That's why you should also don't lerp the speed that much when stopping, it just feels floaty and like you have less control.
The right jump can take forever to perfect, but luckily there's entire talks and papers dedicated to a good jump, and to making and adjusting the perfect curve without having to do trial and error. I recommend you go read up on it, for example how the Super Mario Bros. jump was written, it's really interesting.