Nope. What you're probably seeing is better facilities at higher prestige (*rating) schools which is directly tied to better progression. You're good on correlation, wrong on causation.
As for the OP's questions:
(1) It depends. If you've got all the tuners and updates, it works pretty well. Maybe even too much progression for some stats (SPD). If you don't have the updates, it's broken. And if you've got the updates but not the tuner packages, it sometimes doesn't work at all.
(2) I haven't seen playing time & game states actually matter as far as progression. The devs added in-season progression, but it only effects some players and only adds a couple points, if that. I think it's just based on initial player caliber and also potential (apparently a hidden rating).
(3) What do you mean? Like which attribute effects OVR increases the most? Probably AWR then. If you're asking which attribute effects actual progression, then the question doesn't really have an answer. The devs said "potential" is a hidden rating, but I haven't really seen anything to support that. Seems like we'd see low-ranked "diamonds in the rough" that turn into superstars - but we don't.