I live in Moorhead, but it would be difficult to compare my expenses to yours since we're a family of four living in a house that's bigger than any apartment.
I would guess that you might spend about $300 a month on food, but that's a pretty rough approximation. It also depends, obviously, on how willing you are to live on cheap food. Food prices in Fargo-Moorhead are a little below the national average. Here's a website showing the cost of living index for Fargo-Moorhead and some other cities.
Chamber of Commerce Fargo Moorhead: Community: Cost of Living
The overall cost of living is below average in Fargo-Moorhead, but it is above average for utilities due to the cost needed to heat your home in the winter.
Here's a website showing the rates for electricity and water in Moorhead.
Residential Rates
If you live in an apartment, you probably would not have to pay for water or garbage (I never paid for water or garbage when living in apartments in Fargo), but you would have to pay for electricity. Electricity is $6.95 per month plus $.061 per kilowatt hour. So if you use 1000 kilowatt hours, that would be 6.95+0.061*1000= $67.95 per month. I honestly don't know how much electricity you would use, but I'm sure it would be more than that in the winter if you have electric heat and probably less than that the rest of the year.