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I could also imagine that the "best" counting technique might be differently so that for territory counting in pairs might be better and for area calculating rectangles might be better.
I don't think this could really be the case. Area and territory counting are different ways of ascertaining a score, but the game of Go is unlikely to be affected by more than a point either way, and the optimal counting method isn't going to be affected.
Actually, I don't think any of your questions really depend on how the game is ultimately counted - this is decoupled from the judgement of move value during the game itself. If there is a notable difference, I'd expect professional competitiveness to lead to them all converging on the same one anyway.
Nevertheless, for what it's worth I've heard that most professionals (not just Japanese) tend to count mentally using territory style scoring, since it's generally easier to count territory than all the individual points of the board controlled. I can't provide a source though, so it could just be wrong