About the different randomness sources:
1) Cards drawn during battle: Well, this is kind of the point of the game, so not much one can (or, should) do here.
2) Upgrade card types offered: Forcing the player to adapt is a good idea. Forcing them to adapt to impossible situations is not. This should be much more balanced.
3) Number of coins in a diamond: Why?? Serves no purpose other than making you randomly poorer or richer.
Really fun game! However, beyond level 7 the randomness plays way too big role imho. If you don't get just the right upgrades between levels 1 and 7, it is virtually impossible to go beyond level 10-11, no matter how well you play.
Tips for level 7 (spoilers I guess): get the double jump and use it to get the teleport, without opening any chests. Then use the teleport to move from the top right platform to the leftmost chest first, and from then it's easy.
Really good game, well done!
I managed to do it in 19 days, but luck was definitely involved. I made some small mistakes, so maybe it would have been possible in 17 days. With exceptional luck, maybe even 15 is reachable, but anything lower than that is pure cheat:)