I finally beat it and found all gems except for the "Thank you for playing" stage, but that one doesn't have a door or a gem, I think. Thanks for your help.
My final feedback is that there should be a bonus for beating every stage with a gem, like an extra message at the end. I had fun.
Edit: Also the code to skip levels doesn't work, it only changes my browser tab. I tested it on a desktop computer and a laptop to make sure it wasn't a keyboard problem.