First when GSX recognizes the jetway at an airport, it is necessary as you know that the jetway be activated manually, but how is this accomplished? What key commands animate a jetway?
The default key command to activate a jetway in FSX is CTRL+J. This doesn't have anything to do with GSX, the jetway was always controlled that way, and the GSX installation hasn't changed that.
Is there a file within FSX that needs to be altered?
No, if a scenery has animated jetway, you park at a gate with a jetway and the airplane you use is native for FSX, the jetway will work.
Do third party airports such as FSDT, and others have automatic recognition, and animation of the jetways at that particular airport?
All our airports have standard FSX jetway (with a custom shape, but they work as standard jetways) and there are some 3rd party sceneries that have proper FSX jetways too, like those from Flightbeam or UK2000. All FSX default airports also supports animated jetway.
Other 3rd party airports either have static jetways or use non-standard ways (such as COM frequencies or add-on programs) to animate their jetways.
In this case, if the scenery has static jetways, GSX won't change that. And if the scenery has a non-standard way to operate a jetway, GSX won't change that either: you'll continue to operate it in the non-standard way, as before.
The only thing to note is, if a scenery has static/fake jetways or animated jetways that operate in a non-standard way, you must TELL GSX there IS a jetway there, since GSX detects automatically only native FSX jetways, it can't detect a static jetway, because it doesn't exists, and it can't detect a non-standard jetway. In this case, you want to use the "Customize parking position" option to instruct GSX where those fake/non-standard jetways are, so it won't display front stairs and a passengers bus there.