No, it is not owned by the RAF. It is owned by Air Tanker, who hold the AOC for operating the aircraft and do what the customer (The RAF) ask. The aircraft are maintained by Air Tanker with a pukka 145 approval from the UK CAA with sponsored reservists (LAEs), Civil LAEs, RAF LAEs and a combination of contracted and RAF personel as the mechanics. Management will be Civvy/RAF like the 2 line contracts.
Don't know about pilots (possibly all RAF), and military rules will apply to most operations I would assume (due to role, but the CAA cater for this).