I don't have any screenshots atm but for now I can answer your questions. If I run into a screen freeze again I'll be sure to screenshot it.
I didn't select the save option since I figured I saved by sleeping under the moon symbol. When I beat the chymera blocking the spot under the moon symbol, the screen froze on the fight screen (but I could hear the sounds of the textboxes after the fight?) Also, this didn't happen consistently, I beat the chymera the before and it was fine. Same for the Hide n Pounce, I beat it before but when I did it again it froze (at around a third of the timer left).
For the old chymera, I selected Nap Time, got the Zzz and the defense up, but after that the screen stayed black. As with the other cases I could hear myself running across the map but I couldn't see anything.
Also thank you for telling me where the save option is, this should make the freezes much less of an issue!