Windows 7: Q: Program Compatibility Wizard

I would like to find out more about the Program Compatibility Wizard (and its relations).

Recently I ran a program installer (a .exe file) and on completion the Program Compatibility Assistant advised me that the program may not have installed correctly. One option was to "reinstall using recommended settings" but the program seemed OK so I clicked "This program installed correctly".

I would like to know:
a) Will Windows 7 do this check each time I run that program?

No, it only does that when you install something, and I think there is even a tutorial on this site to disable that.

b) How do I find out what the "recommended settings" are? The [i] button "What settings are applied?" was no help.

I could never figure that out either.

c) Where are the compatibility settings stored? From this tutorial Compatibility Mode they may be stored in the .exe Properties; but is that is the .exe file itself or somewhere else?

I believe they are stored using registry keys.

d) how do I undo any Compatibility settings that are assigned by the PCW to a program - do I just edit the settings in the .exe file Properties tab?

I'm pretty sure that's all there is to it.

e) Can someone tell me what the entries in this Registry key mean?
[HKEY_USERS\S-1-5-21-xxxxxxxxxx-xxxxxxxxx-xxxxxxxxxx-1003\Software\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Compatibility Assistant\Persisted]

"F:\\DarkStar\\Documents\\Apps_01\\releases\\software\\prog_v3-install.exe"=dword:00000001
-- and a few more similar lines
-- I've replaced the key numeric values with xxx in case that is sensitive info
-- I am tempted to think that this indicates Programs that have been confirmed to have run (installed) correctly.

I'm not sure about that one. I'm pretty sure that's NOT where the settings themselves are stored though.