Congratulations on your new camper.
I can't answer the first question, but yes you want to remove the battery and keep it on a trickle charger for the winter. Actually, you should remove the battery, if you don't have a battery disconnect, any time you won't be using the camper for more than a few days, certainly more than a week, if it isn't plugged into shore power. The radio and the propane detector both create a "phantom draw" that will drain the battery pretty quickly and batteries that are drained too low will lose their ability to take a new charge.
2015 Bullet 220RBI
2019 Chevy Colorado extended cab V6 3.6 liter