Some nice ideas but a bit confusing. I can teleport anywhere anytime? I ended up mostly just teleporting to grab stuff and not walking at all. Took me some time to figure out why sometimes I could dash and others I can't.
There's a bug where sometimes a gem doesn't disappear when collecting it and it starts collecting it forever on a loop!
On second part, the background moves with the player even though the screen is fixed, which makes it look quite weird!