For sure - It's pretty quick, I think it's on the same line, or you might have to change in Kassel. Should only take a couple hours. I think an ICE fast train runs there.
Maybe 50 Euro? Check out bahn.de I think you can figure out what it costs there, and get a schedule.
You could get a BahnCard 100 which allows to take any train (except for the ICE Sprinter) as many times as you want at any time you want. It costs about €3,500. But yea, in the long run its cheaper than paying €50 every time.