It’s the third one: I cannot select the gates in either method.
If even the default "Go To Airport" doesn't list the correct gates, the problem doesn't have anything to do with GSX, and it's caused by another scenery in conflict with your airport.
Even if the problem doesn't have anything to do with GSX, it might still be used to check which scenery is causing the conflict, by checking the GSX parking customization page, which will list the AFCAD used by GSX, which is supposed to be the one that comes with the airport. If it's not, you might have some idea which is the conflict scenery.