is there a train that goes directly from Hanau to the Frankfurt airport, or will I need to have time to transfer by taxi or?
Also, since Frankfurt is so busy, how early should we plan to arrive?
The ICE coming from Passau and Nürnberg also stops in Hanau on it's way to Frankfurt. Sometimes it goes directly to the airport, sometimes in terminates at the Hauptbahnhof downtown.
Careful though, the ICE fare is 16 euro, the S or RE fare 7.80 euro. There are a few RE trains that are direct in 25 minutes, but if you arrive at Hanau, your next direct departure is likely to be the S-bahn, about every half hour, and every 15 minutes during rush hour. There tons of other trains requiring a change at Frankfurt Hbf.
Gute Reise!
If you use the www.rmv.de website, you will get all of the train connections from Hanau to the Regional train station at the airport. As already mentioned, the ticket is 7.80 €. Duration of travel time is between 33 min. and 48 min. The longer train rides mean that you will have to switch trains at the Frankfurt main station. Suggest you avoid that by just waiting on a direct train that runs every 30 min.
As to what time to get to the airport, if it is a flight to the states, you should plan on arriving at the airport 3 hours before departure. If it is an inter-Europe flight than 1.5 hours is sufficient. I always add a cushion of time simply to insure that I am there on time, leaving space for train malfunctions, etc.