Is it allowed to pause and quit the current level during cutscene ? If yes, can it save time on some level ?

Sorry for the late answer.

Back on the first days of this game, it was agreed to ban that and it is mentioned in the rules too.

As for the reason, I can't recall it exactly, but since those cutscenes have interactions (having to mash to proceed with dialogues) it makes sense to include them as they are not mere autoscrollers since anyone may not have the same mashing speed.