Experienced Botox injectors have great success with the crow's feet. As usual, best to be conservative; you can always add more.
Yes, if the forehead injection is not ideal, the Botox can spread downward and cause the muscle that keeps the upper eyelid "up" to weaken and hence the droopy upper eyelid.
This is rare. It can also occur when injecting to position the outer eyebrow. It is possible to raise the outer (towards the ear) portion of the eyebrow by judicious Botox injection. That takes a expert with long experience. If that were done imperfectly, the same problem with the upper lid could occur.
Since you are most concerned with the crow's feet, tackle those first.