In the Squid Game, how does the doll’s head move?
The doll’s head moves when a trigger sends a signal.
However, even though the trigger sends a signal,
First of all, don’t worry about your English level! It’s really good!
Regarding your questions, I’ve been researching about that Prop Mover and I can tell you that is not the best way to rotate an object! Actually, one simple and more effective and controllable way to do that is by using a Level Sequence with the Cinematic Sequencer Device. Here is a video tutorial that I found really useful to do that: https://www.youtube.com/watch?v=Cev4-DOKaRA
And about your second question, every Prop that moves using the Prop Mover will damage the player on collision. What is happening with the Doll is that its rotation is damaging the player if it is close anough.