Our fridge did not have a freezer in it.
The chairs on our balcony were a full size lounge chair, a regular chair, and a low-to-the-ground chair that you could put the back down on. Ive heard that you can tip your cabin steward to bring you another lounge chair.
They have free movies that play but I never saw the option to rent any. Since the cabin has a VCR if I were you I would take some movies for the kids.
The balcony railing was pretty high and goes all the way to the floor. I think its very safe. It would be very difficult for someone to fall off - they'd have to climb on a chair to get high enough to fall.
I just remembered another tip - the cabin only has one obvious electrical outlet (with room for two plugs) and its in the dressing area. We discovered that the one the tv is plugged in can be used if you carefully move the tv (we had to move the plug to the top outlet in order to get our digital camera dock to plug in).
Let me know if you have any other questions.