Today I saw a Qatar Airways 345 in CIA, anyone any clue what it did there?
It can't have made it to Qatar from CIA with a full load anyway. I doubt CIA has the facilities for non-Schengen flights.
The QR A345 is from what I know a VIP aircraft. So I doubt that loads and Schengen issues will have a big effect on them. They're probably using CIA and not FCO for cost reasons and to avoid heavy ground traffic I presume.