All 101 Sqn crews were cross-qualified on the VC10K2, K3 and K4. But as the K2 became increasingly scarcer, there was little need to cross-qualify the 10 Sqn people unless they were going to fly the K2 in the sun-drenched Islas Malvinas.
A few minor differences, but nothing really significant apart from buffet speeds and the 177 knot flap limit beyond the 'take-off' (20 deg) setting. Often the TPI would be right at the 7 deg limit at max TOW; the aileron upset applied as soon as the flap lever reached the front of its travel (unlike on the K3/4), so the process of accelerating after a max weight TO to achieve flap up safety speed needed precise control.
The C1K is indeed a hybrid - not a 'true' Standard VC10.
K2s went out of service only because they were old. Plus, when some wretched engineer decided that the 'fail-safe' design philosophy was no longer acceptable in the 1990s, the allowable flight envelope (AFE) for the K2 to operate within 'damage tolerance' margins became severely restricting. But with a little research and effort, I was able to devise a long-range cruise technique for the old dears which meant we could make MPA-ASI in one hop - and also ASI-BZN. Take-off and climb with 'max allowable noise' until reaching the initial cruising level of a mere FL170; you then nibbled up the edge of the AFE as weight was burnt off until reaching FL290. Where you stayed until you had got down to a weight at which you could make FL370. There was no earthly point in cruising above FL290 unless you could make FL370 as the requirements of the daft BWoS AFE would have meant cruising with aileron upset applied - and that drank more fuel than cruising at FL 290 without. Having reached Real Mens' World of FL370 where the air is rare around 4 hours after take-off, you stayed there until top of drop at a sedate IMN of 0.82. That way you could get 9 hours flight time from take-off by which time you'd be at DH with 7 tonnes remaining. Flew the profile 3 times and it worked a treat - saved HM the Q landing fees at a couple of en-route aerodromes as a result and got the team home a day early. Did anyone say well done? Did they hell....