Finally I can share my experience.
I parked my car for 02 days at the new Islamabad Airport long term parking.
The place is near the entrance to the parking area and is closed by a chain. It is not very secure and they give you a receipt that clearly shows "park àt your own risk".
But after 02 days I got my car without any problems. Had to pay 400 per day. The person working there told me that a covered larger parking area is planned to be built.