A Couple Of Questions Regarding DB Rail

I need to book round trip rail from Frankfurt Airport to Stuttgart main station.

1 - Is the Frankfurt Airport station called "Fernbanhof"?
2 - Is the Stuttgart main station called "Hauptbahnhof"?

Assuming both of the above are correct should I book rail now for January 2012 travel or just wait until I arrive in Frankfurt? Is there a savings booking in the USA vs in Germany on arrival?

1. Fernbahnhof means long-distance railway station.
2. Hauptbahnhof means main railway station.

There are two stations at Frankfurt airport (fairly close to each other).
"Fernbahnof" is the long-distance station, for ICEs and similar trains (including some direction connections to Stuttgart).
"Regionalbahnhof" is the local/regional station, for trains into Frankfurt centre (from where there are other connections to Stuttgart).

Yes

It is probably best to book online at bahn.de. If you book well in advance, you may find an ICE from Frankfurt Flughafen to Stuttgart for €19. Meanwhile, if you buy the ticket on the day of departure, it will cost €57. However, the discounted tickets restrict you to a specific train, and have a penalty for changes/cancellations. The €57 fare is fully flexible.
If the buy in advance fare is not available (or the price is too high), you may find cheaper, but slower, connections via Frankfurt Hauptbahnhof (try the "all except ICE" search option to find these connections).

Note that if you're flying into Frankfurt, then you will need to leave plenty of time between your scheduled arrival, and the departure of your train (especially if you're on an inflexible, buy in advance train ticket).

I posted some similar questions this morning before checking this thread. Very helpful.