Engines, from my vague recollection, the ASK21s (Vanguard?) were on the military register from the outset. Certainly they arrived at RAF Syerston/Catterick with ZD64* stuck on the tail. That would have been in 1983.
Filling-in bits of your other questions:
Q4 - Training Command disappeared in the mid 70s so for the introduction of the 'glass fleet' in the 80s the initial responsibility would have sat with Support Command. There were no defined Group formations within this command. Support Command was then split in the mid 90s (1994?) with elements being split between Personnel & Training Command and Logistics Command.
Q5. Again, a vague recollection, but the RAF would send maintenance teams (Cpl-Chief Tech) routinely about once a year to do annuals etc. If we bent something, we would park it in the back of the hangar and await the RAF chaps. For example, we had the authority to do things like tyre pressures but not tyre/wheel changes.
Sorry it's only a snippet.