I think it is possible with the right candidate, simply because Wyoming is so small.
I don't know about that. Even if the Democratic Presidential nominee was from King County TX, they'd almost certainly lose their home county.
Wyoming and other states in the area like the Dakotas or Montana are different than Texas or the South. Democratic candidates have to deal with a lot of baggage there that they probably don't have to deal with in Wyoming. I would say that while Wyoming is probably the most republican state, it's also a lot more elastic than Alabama or even Mississippi.