Hot water and heat are centrally supplied in UB and they are rarely interrupted in winter. Control over your heat and hot water may not be so good. Many buildings are over-hot in spring and fall. Hot water may range from tepid to scalding, sometimes in a matter of minutes.
Electric outages seem to be dependent on where you're living in the city - I worked near where you'll be living for my first year in Mongolia and power outages were not very common. As best I can recall, it was unusual to have more than 1-2 outages a month, and usually for less than an hour or two. In two years living in UB, I remember only 2 long power outages, one about 6 hours and one about 8 hours. Irritating but not a big problem.Â
I did find it necessary to have candles, flashlights and a small single burner portable gas stove. We used the gas stove for hot-pot meals as well as power outages just before dinner.
Area near the campus of MUST university is convenient. For expat shopping, you're near both the Sky department/grocery store and a wide variety of restaurants and other stores, and a cinema.