As of 4.1, yes (sort of), no, no, and no. And aside from a cutscene or two during the mom's questline, no. If you'd like to see all the possible cutscenes without the work or not caring about spoilers, google breeding farm debug codes. One of them unlocks all the cutscenes in the gallery, but the ones that come from breeding between the mc and monsters will not play in the gallery (but it will show which combinations will produce scenes which is helpful).