Great job on your first game jam! Congrats!
I've seen a few of the "self-destruct self" to advance games already, but yours does the best of getting the player right back into the action by making the respawn close to the start and keeping the level short. Good call! You're already aware of a few issues with the game. I gave up on the climb level (3?) just because I couldn't get the physics of the bodies to work in my favor. Perhaps locking them in place while the player is airborne might help? That would allow you to push them and reposition them, but not worry about losing your footing while jumping on them.
Overall, well done on your first foray into jams and Unity. Keep making games!