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The resistive track on the pot looks damaged (big scratch on the left side), so the pot may be useless even if you could re-attach the connectors :(. Pots are relatively cheap: is it worth trying to repair that one?
Wow! Cheaper to use a gold contact and sell the platinum! Gold is easy to solder, but I don't know about platinum. I'd try ordinary resin-cored tin/lead solder first. Do you really need a precious metal contact?
With 4 legs it could be a switch, or a pot with a switch. Can you feel detents when you rotate the shaft?
If it's a pot it will have some numbers marked on it. Tell us what they are.
It might do. Why risk it? You could drop the volts down with a couple of silicon diodes (e.g. 1N400x), or else just buy a proper adapter. Welcome to EP!
Welcome to EP!
What is the 'particular device'?
Can it be modified?
Will it accept output from a 'modified sinewave' type inverter, or only from a 'pure sinwave' inverter?
What is the aircraft supply voltage?