Many thanks for playing and your extensive feedback, wow! I'm glad you enjoyed it. Selecting enemies was not intentional, so thanks for the bug report, too.
Level progress should actually be saved between sessions. It does work for me on some devices, so unfortunately I don't know yet why it can fail. I'm sorry this didn't work correctly for you.
Yes, the "unexpected pit" in 1-4 is intentional but could be more clear, it's true. All other points I'll definitely consider for further updates.