To your knowledge - I also have a MacBook Pro Late 2012.
If I "Duplicate" my Applications Directory - the copied version is empty.
If I try to Burn the Applications dir on CD/DVD all I get is a "The source dir is empty" errormessage.
But I can type a programm name into spotlight and get it listed, I can also run that programm - so its on the disc.
In the spotligt result window, I can also grab the program icon and move that to another folder - and the program is listet there with no problem I can also run it from there - but the original entry is still in "Applications" when I do a " ls -l /Applications " in Terminal.
I can also use the programm "AppCleaner" and get all programms listet there - so I was able to remove all the old ones that are incompatible - but it didn't solve the problem.
What I just found was, that if I try to search for "Festplattendienstprogramm" (german for "DiskUtility") - this is not found, but it looks that the finder crashes while spotlight is searching for that.
I also get a lot of incorrect a group rights errors like:
Abweichende Zugriffsrechte für „Library/Java“, Soll-Wert: drwxr-xr-x , Ist-Wert: drwxrwxr-x .
Gruppe von „Library/Preferences/com.apple.alf.plist“ ist 0, korrekt wäre 80.
Der Benutzer von „private/var/db/displaypolicyd“ ist 244, korrekt wäre 0.
Gruppe von „private/var/db/displaypolicyd“ ist 244, korrekt wäre 0.
So maybe there's a problem too.