Hi there, Courtnay! Welcome to the Disney Parks Moms Panel!
I can answer the first half of your question easily: all Resort hotel rooms at Walt Disney World are equipped with either a mini-fridge or, in some cases, a full-size refrigerator. It's so convenient to be able to stock up on cold water, sodas and snacks in your room so you have what you need right when you need it.
As for microwaves, they're not as common, but there are rooms that include them. The family suites at Disney's Art of Animation Resort include a kitchenette complete with mini-fridge, sink, microwave and coffee maker. There are also family suites at Disney's All-Star Music Resort that include the same kitchenette amenities.
Another option is the Cabins at Disney's Fort Wilderness Resort & Campground. These include full kitchens, with a full-size refrigerator, microwave, coffee maker, sink, oven and even a dishwasher. They also have a grill outside on the deck. The cabins are great if you want to cook full meals for your family.
If you prefer a standard hotel room, I have a couple of suggestions. There are microwaves available for Guest use at the food courts in the Resort hotels, although this would mean you'd have to leave your room to heat your food. You can also try calling the hotel you'd like to stay in and see if you can request that a microwave be delivered to your room for your stay. I'm not sure if they do this anymore, but it never hurts to ask.
I hope this helps you find the right room for your family, Courtnay. Please stop by and visit us again if you have any more questions.
Have a magical day!
Kathy K.