Can I somehow export/backup my Adobe Photoshop settings?
All the stuff in Edit -> Preferences
Depends on your system, depends on your version of Photoshop.
Say you're on Windows and using Photoshop CS3.
Head yourself to this location:
But if you're on a Mac:
Copy all the contents of that folder and that's all your preferences. Next time you re-install, just drop these files back into the same position.
Tweak as necessary for your setup.