Fair reply
You've answered your first question straight away, so yes. It was a foul. correct decision
The responsibility should lie with the ref not VAR, if he deems that not much of a foul in the context of the game then it's on him to ignore the VAR and it's on him to make the ultimate decision when seeing it on the monitor.
I personally think there is a difference of allowing some argy bargy go throughout the game but when it leads to a goal then the correct decision has to take precedent, think we've seen that in the history of the game - a couple of challenges go unpunished in the middle of the pitch or waved play on, but in the area it's given a penalty no matter what (for example)
I'm definitely in favour for comm's/transparency argument - not sure it would solve much but still be good to know what was said.