There almost certainly would be taxis or Uber/Lyft available at that hour, especially on weekends. Both Fargo, ND and neighboring Moorhead, MN have large colleges, and 2 AM is bar close time. At most you might have to wait a bit for them to finish up a run, but they should still be out and about. There are a few hotels within a few blocks that could be walkable as well.
As for hotels, you'd have to check with individual hotels. However, I wouldn't expect there to be any with shuttles to/from the Amtrak station that early in the morning. The bus service in town also doesn't run overnight.
Are you planning on renting a car once in town, or just exploring on foot and supplementing with Uber/Lyft? If you're planning on the latter, I'd suggest staying at one of the downtown hotels, as there's a decent amount of things to walk to in/near downtown.