Thank you for your feedback. The reason there is only one way to solve the 4th level is that I wanted to increase the difficulty at the last minute. I was looking for a solution that takes as few moves as possible to make the puzzle less obvious.
I didn't find any problems with the move counter during fast movement. Maybe you were referring to the fact that when you reach the cat, the transition to the next level takes 1 second, and during this time you can still move. If you move at this point, the level will reset because you will take a step when you have zero moves. This is a flaw that I am aware of, but I didn't have time to fix it.
Thank you again for your feedback. I plan to improve this game to release a version with at least 10 levels and generally polish it.