Quite often when I’m viewing a cutscene, either before a mission starts or the ending cutscene of a mission, I don’t reliably get the ability to skip it.
Sometimes the ‘Press (Y) to Skip’ message just doesn’t come up at all, pressing (A) it just says ‘Loading…’, and often just displays that for a bit before disappearing. Pressing (Y) after it goes away usually does nothing, and pressing (A) again just has it say Loading… once more.
When it says “loading” it’s loading the map, so if you were to skip it, you wouldn’t be able to do anything since the map wouldn’t be loaded
The only cutscenes that have that loading thing that you can’t skip that you can skip are the end level. If you hold A and Y as the screen fades until the second loading screen shows it skips the cutscene. As for the other issue sorry but you just have to spam A and Y until it shows up and skips