Welcome to the forum, GreekChic. I'm sure any locksmith can make a key for your lock. If you take it off the door and take it in that will simplify things. But, you could probably just replace the lock with a new one and you'd get two keys for it, probably cheaper. They are available online. Suggest you look in etrailer.com to start.
Your battery should be a 12V "Deep Cycle/Marine" battery. They are available many places. I buy mine at Costco. You just need one that fits the space.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew