Now listed elsewhere

You might be able to fix the loose cage rivet by doing this (via @PhilDAS on a different thread):

Bottle cage mounts are rivnuts seated in holes drilled in the tubing.
They're gripped in place and can come loose. You can put a skewer
through a hub, screw it into the mount as far as it will go and then
tighten the skewer. This pulls it in on itself and grips the tubing again.

I'm really keen to try it, sounds like a great hack!