You do regain your health when you pass level. There's also a checkpoint after each level, there are only 2 of them though. On stage 2 there's a tutorial on how to fight.
There are levels because it's a rhythm based game and each level has a unique song and beat, a endless stage would get pretty repetitive. This is also the reason why there aren't checkpoints mid-stage, they would break the flow of the song.
A shame you didn't like it, but it is a pretty hard game and not for everyone :(