>> "Does the TurboFloat service need to be hosted on a "real" computer (i.e. they would need to run TurboFloat on their premises, rather than in the "cloud")?"
Yes, because the TurboFloat Server needs to be activated to run. And if they host it on EC2 as well (or any other VM service where the VM moves from computer to computer) then the TurboFloat Server itself would become deactivated.
So they should run the TurboFloat Server on a real computer on their network.
>> "If so, if the TurboFloat service is behind a firewall, do they need to set up some port forwarding so that our (TurboFloat enabled) software can connect to the service?"
Yep, TurboFloat needs to be able to talk to the TFS instance. So, if there's a router, firewall, or anything else in the way, the correct ports need to be setup.