first: THANK YOU for linking to videos in your post. i really appreciate that, and it makes it a LOT easier to diagnose.
for 1 – i agree with you. i think she’s focusing on the “prey” with her odd head movement. i’ve seen this before in a healthy cat.
for 2 – maybe? i’d wait and see on it, honestly. if this is only during walks and play it may be behavior-related rather than health.
Take him to a vet asap !
This is one time we can all only say take him to the vet and tell then it’s urgent.
Sorry to hear
Might have parvo
That’s what happen to my puppy found out today she had parvo best of luck !