It will always be difficult to what extent it is the managers influence and to what extent it is natural development but the ability of a player certainly changes over time. Maybe it could better be described as shaping a player to a certain role - like Pep did with Sterling for a while, what happened to Ronaldo under Fergie and even more visibly at Real.
I think point C is certainly true and is ultimately what management is all about.
That and having a good eye for talent in the first place.
Point A and B I'm not sure about. Never been convinced a manager can increase a players ability. A player is what he is to me.
Ole had a dynamite front four for a short spell. Greenwood coming and seeming to score with every effort for a while was a huge boost.
Just a huge shame he couldn't strengthen when all was going well. He should have spotted that even when playing well, Martial was not the option long term.
It is obviously difficult to really pin point, but for me, the best spell of Ole was mostly connected with a) the players being freed up from Mourinhos negativity, b) many opponents not taking us seriously and still having a go at us while we relatively quickly became a very potent counter attacking weapon and c) in regards to Greenwood having an unknown entity that no team was prepared for while producing numbers like an established part of the team. I personally don't think, that had anything to do with Ole being a good or a bad manager - I think, from a character and status standpoint, he was the perfect fit to take over mid season because it had several positive effects. But I hardly doubt any of those effects had anything to do with his abilities from a football coach perspective. He was a great choice for the interim role and he did a really good job - the issue was sticking with him hoping that those effects would continue to last.