I am not sure which fridge you have, but the draw on the battery from a fridge will be fairyly high.
This all depends on many factors such as how cool is the fridge before you dry camp, how warm the outside temp is, how often the door is opened because of the light and the cool air in the fridge will escape.
Normally we camp at water and electric sites. The one time we dry camped, we were able to run the fridge and a few lights off the battery for the day. We left the next morning so I can not tell you exactly the current draw of the fridge using the battery. There will be other dry campers that can help you better with your last question.
HAPPY CAMPING!! :D
Daryl and Sandy
2013 Eagle 314BDS
2012 Ford F150 Platinum, 4 x 4 Crew Cab with Ecoboost