We also have the outdoor fridge at the back of the camper. I fill it up all the time before we leave home but every single can/bottle is laying on it's side or stacked like hay bales, not standing. I've arranged the shelves so that there is only room for 1 or 2 rows of cans high. It's actually better to have it FULL than empty, less movement.
Outdoor fridges are usually dorm type fridges - shore power only. I saw a discussion on another board about how difficult it would be to get a propane fridge in that spot - because it needs venting, etc and the back of the fridge is the outside wall of the trailer - aiming in.
I love my outdoor kitchen, but did not see much use for the fridge, since we do not drink soda or beer. I had it removed and now have a good piece of counter space for appliances I do use.
If you want to stick things with double sided tape, get the 3M mounting tape with the red backing. It's the stuff you stick vent visors and bug deflectors on with. If the surfaces are cleaned properly first, it'll stay stuck.