You're reaching forward and holding the pole there for a split second before you plant. i.e. You lower your pole to horiz, pause as you reach, drop it to complete the plant, jump ...
Holding your pole in that horiz position causes you to lean back in your last couple strides, which causes all the subsequent faults.
Try dropping the pole into the box in one motion - no pause. To do this, delay the initial drop a bit. Work on it on short runs, then move back to full run.
Also, as already pointed out, your pole carry is too low. Bend the elbow of your left arm more, for a higher carry. That way, you don't have so far to plant, and you can work the timing of your plant into the timing of your jump a little better. You don't have to reach forwards as much as you do either. Planting in one harmonious motion should fix that, but it will take time, so be patient.
As far as dropping the head back, there's no good reason for that, other than at some point you or your coach must have thought that it was a good idea. Now you know it's not. Do what Amy does on the rings, and you'll discover after a few thousand reps that your head just naturally sits on top of your shoulders - not looking down or up.
I don't think the head problem is caused by anything before it, but it sets up the dominos for lots of bad things after it. You do need to fix that! First in the gym, then on short runs, then on full runs.
This is all academic, of course, since the vaulter in question was a one-time poster.