I’d like to plan a dinner at a restaurant in the park where Mini can bring a cake to my granddaughter after the meal - is it possible to make that kind of arrangement?

I don't think so but you may enquire there

I know that it is possible in Paris, in the village. Try perhaps something like that in Disneyland LA.

Sorry No idea

Call 714-781-DINE. its Disneyland's restaurant reservation line. They would be the one's to ask if it is possible

you should call the park info they are very helpful. but I think some of the restaurants by the hotels might be able.