1) Zurich and Chicago not installed nor scenery activated
Please, clarify what do you mean with "not installed" or "not activated".
Not installed means the scenery files aren't on the hard drive anymore and/or the scenery was removed from the Scenery Library. This CAN'T simply happen to Zurich/O'Hare by just *installing* JFK. JFK installer doesn't remove any files from these sceneries, so it's impossible that after JFK installation, you have KORD/LSZH "not installed". Unless, by "not installed" you mean something else.
Also, please, clarify what do you mean by "not activated".
Not activated means you lost your hardware activation. When losing the activation (this can only happen with a change of hardware), a scenery reverts to Trial mode. This means, it will run perfectly, for 5 minutes. If you lost your activation, the Addon Manager will say that scenery is in Trial mode. If the Addon Manager says the scenery is activated, you haven't lost your activation.
Unless, by "not activated", you mean something else.
2) Installed JFK. Scenery got activated automatically in the scenery.cfg
Of course.
3) Used Addon Manager to purchase JFK, and I got confirmation "scenery is now active"
That's normal.
5) I had read something about installing the FSDT airports in a certain order, thus:
The order of installation is entirely irrelevant, provided you already have the current installers that gets all the crucial files of the Addon Manager from the internet. The order of installation *might* be relevant if, for LSZH or KORD you still had an older installer, with no internet download of the Addon Manager files. JFK has been released only with this new installer type.
7) Installed Zurich and activated it manually (no automatic activation)
What do you mean, in this case, with "automatic activation" ? Activation is something that usually is done only when changing hardware. Unless, by "activation", you mean something entirely different, like the automatic addition of the scenery to the Scenery Library.
If the scenery wasn't automatically added to the Scenery Library, this is usually because there's was already a problem with your scenery.cfg, but the installer should have issued a warning about this.
IN THIS CASE, the installation didn't complete, and no files for Zurich were copied (only if you had the warning)
10) Started FS: all three sceneries are in trial version. However, Addon Manager confirms that all sceneries are registered, and there's no possibility to re-enter the code.
Please, clarify what do you mean by "Trial mode"
Trial mode means that the scenery runs perfectly for 5-6 minutes, and when you go to the airport, you'll see a message stating "Trial mode for zzzzz starting". Trial mode DOESN'T mean you don't see any scenery!
If the Addon Manger says the scenery is Active, then is active. If you don't see any scenery, it means the scenery hasn't be added to the scenery library OR, since you said you had to add it manually, it might be because the installation wasn't completed because a problem with scenery.cfg. You should have seen a warning coming from the installer, so you are addding to the library an incomplete scenery
First, your problem doesn't look like to be something related to activation/registration. And, it seems you ARE able to run the Addon Manager properly, so we scratch any simconnect/antivirus/firewall issues.
I think you should simply start from scratch. Please do exactly as I've said. Don't do anything else.
1) Ensure you have the current installer for all 3 sceneries. If unsure, download them again.
2) Uninstall all 3. Reply YES to the questions about removing the Addon Manager
3) Reboot
4) Ensure no bglman* files are left in the FS9\MODULES folder. If any of them is still there, manually delete it.
5) Install Zurich, launch FS9, check the Addon Manager runs, check the scenery shows. If you don't see the Addon Manager menu, don't do anything, simply exit and try again. If you SEE the Addon Manager menu and it says the scenery is Active, but you don't see the any scenery, STOP HERE, because something is already very wrong.
6) If Zurich works, just install KORD and then JFK, they should work.