If you feel comfortable in assisting him w/the applications and have no expectations, then I see no reason to say no since you've been doing them for a while...but he's got to learn how to do them for himself at some point, i.e., especially if there comes a time that you officially end the marriage.
Sounds like the GF is just a convenience and he doesn't want her to know his business when it comes to his past employment activities, etc. Is he trying to get a private or Federal Government firefighting position?
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.