The speed difference between runs seems to differ between pc's for some unknown reason. I noticed that my game was much slower than some others, but then I switched to my desktop pc and it wasn't slow anymore. Playing on the browser version also fixed the speed issue while I was on my laptop, so that might fix it for you.

The fast transition between levels is done by using the reset button on the keyboard (R button). At a certain point in the animation (first frame of the first star appearing iirc), the character has already entered the next stage. Resetting at this point will instantly put you into that next level, letting you skip a big chunk of the cutscene if you time it right.