The customer insists upon refrigerating the cake, although I have told her it's not necessary.  Should I even go there with fondant decorations on a cake covered in bettercreme, or should I use modeling chocolate?

AFondant will just go flat, but maybe gum paste?

If I use flat fondant decorations, like cut-outs, that will just be on the top of the cake, do you think they will be okay?

The fondant will harden in the fridge, so modeling chocolate or gum paste may be better