For the strap button, I believe the technique would be to put some toothpicks or something similar in the hole (for the screw to thread into) and then put some glue in there, screw it back in there, and you should be good to go. Though I'd wait for someone with a bit more experience to confirm that since I am only like 80% sure on that.
No clue about the detuning though. Hopefully it's ok.