Q.1 For the movement, I thought it was so much fun figuring out new mechanics! I do think that the main things that stuck out to me was starting to move from standing still. It is a very slow slide forwards. I also think the aerial movement was a little hard to deal with as well. One thing I was thinking of as well was making the grapple hook dislodge after un-clicking, rather than clicking once for each mechanic.
Q.2 Personally, I thought the fog was a great challenge starting out, and I had a lot of fun staying engaged the whole time. An experienced player might find it slow once they get good enough. Your idea of having the fog move faster after each level would be nice.
Q.3 I had a really hard time understanding the part in the second level, where you have to traverse the stones that get taller and taller, and didn't really get that you had to start moving left to get momentum going, to get over, which kind of circulates back to my first point.
Q. 4 Instead of enemies, I feel like floating obstacles or flying bats would be a great addition.
Q.5 From when I played, I didn't notice anything that was weird.