Yes, you can have a microwave and refrigerator in your room. But there are size limitations, so don't plan on bringing that huge side-by-side fridge to hold your food and bevs. Your refrigerator can be up to 35" tall and draw no more than 1.5 amps of power; your microwave cannot exceed 800 watts of output power. So basically any smaller microwaves or small fridges you can buy at one of the big box stores will work just fine.
But here's the scoop on appliances you can't bring: any items with heating coils, i.e. toasters and toaster ovens, hotplates, electric fry pans, electric heaters, George Foreman Grills, electric blankets, Halogen lamps or any Halogen bulb gadgets, heating/immersion coils, non-UL listed items, and any electrical items not approved by the Department of Housing.
Some electrical items you may want to consider bringing are a fan, a power strip or surgeprotector, and an extension cord (UL listed, of course).