My GSX shows in my add-ons as "active" but it does not show in my scenery library.
GSX is not a scenery, so it's not supposed to show in your scenery library. However, to get GSX back, you must INSTALL GSX.
My airports show "active but not installed in scenery library"
"Active" simply means your activation is still valid. As explained many times already, you don't lose your activation by just reinstalling the sim, the only way to lose the activation and be forced to reactivate, is to reinstall Windows OR change hardware. The activation status is NOT linked to the fact the scenery is installed or not.
But of course, sceneries are sceneries, so they are supposed to appear in the scenery library. Which means, to get the scenery back, you must REINSTALL THEM.
Basically, when you reinstall FSX, you must reinstall your add-ons too, just restoring files and folders from a backup won't work, and this is valid for most of the add-ons, not just FSDT's.
Just download all the current installers again, and install them now.