Thank you for taking the time to write detailed feedback!
I would have loved to introduce the mechanics a level per level basis to ease the player into them, but I was unsure how to do that effectively. Therefore the one page in the menu. I'm not sure if splitting the mechanics to different sites would have helped, my guess is that would fell even more daunting then before, because you have multiply pages.
I didn't explicitly wrote in the introduction that the Souls had to be "pushed'' into the gate, that is true. I can see where this can lead to confusion.
Souls getting stuck was sadly somewhat common, I thought I had fixed it by allowing the Keeper and Dog to go a bit below the bounds of the souls, but likely I forgot that above.
Interesting bug you discovered with resetting the stages :D