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.
YES, she’s too old – this would be like your grandmother having a baby. it’s not healthy and puts her at significant risk. spay her NOW before it’s too late.
seriously. get her to the vet tomorrow morning and get her spayed.
The humane society offers lower-cost spaying in some places, call them up.
There may also be a pill your vet can give you, but I’m not sure.