Frankfurt airport to Frankfurt train station

Yes, but a regular ticket would cost far less (€3,70 pP) than a day of your railpass. But, of course, if you are already using the pass that day, or if it is global pass, go ahead.

Some trains to the Frankfurt Hbf will be express trains, and will leave from the Fernbhf, which is a ways from the airport terminal. The trains are faster, but the walk probably makes up for the difference. Regional trains and S-Bahn leave from the Regionalbahnhof, which is under the building across the street from Terminal 1.

The S-Bahn runs every 15 minutes. Most S-Bahn trains go through the Hbf Tief (deep) station. You'll have to come up several levels on escalators to reach the street level.

Yes, you can but don't use it unless you are catching another train because any time you use it you use a day of travel. But you may not need to go to the Frankfurt train station since many trains leave from the airport train station.