The remote fobs and built-on remote on the one key should all be programmable by yourself if they all still work, have power in their batteries and are the correct ones for your car, there is a code printed on the circuit board inside, these should all match. Details of process to program them all to the car are widely available on internet and youtube.
The lock on the fuel cap is purely a physical contraption your keys either fit or dont, probably your key or the lock in the cap has become worn or damaged enough for it to not turn the lock, can't see there is anything you can do about that unfortunately.
I assume (but DON'T know as a fact) that these keys have a transponder or chip of some sort that connects to immobiliser, guessing further your immobiliser is not programmed to receive one of the keys (or the key chip is damaged), I'm not aware of any way to reprogram these yourself without forking out £££ at a honda main dealer, probably not worth the bother.
I did read something on line about disconnecting the battery for 20 minutes, it was a bit vague but stated the electronics then try to reconnect to your keys.
Possibly worth leaving things as they are in case things get worse by tampering, at the moment you have 2 complete sets that allow you to open, start and refuel.
Good Luck and keep us updated.