I noticed that this website offers cheaper tickets within Germany. Do you know if they are a trustworthy company? Has anyone dealt with them?
Which website are you speaking of? Cheaper than where else?
I see that there is a site called GermanRailDirect.com. They are associated with Wandrian and, I think, RailPass.com. They have been around a while. They use the ticketing service of Trenitalia.
However, they don't have the cheapest tickets! I looked up Frankfurt Airport to Munich and they showed $133 which is about the same as what the German Rail website charges for the ticket, full fare. If you are willing to book ahead, online, which is what you are doing with GRD, German Rail will sell that ticket as a Dauer-Spezial for as little as $45 (€29). For the date I checked, the $45 ticket were sold out, but I did find them at under $80 pP one way. Plus, with German Rail you can print the ticket on your own printer for free (GRD wants a minimum of $14 shipping), and with German Rail your reservation, at the time of ticketing, is only €2 (vs $11 from GRD).
Use German Rail.