Presumably both airshots and the argument crop up pretty regularly?
If you take airshot to mean a stroke that misses the ball, then the answer has to be no. Whatever the reason, the stroke counts.
If your clubhead falls off in your backswing and you continue with a downswing, it isn't considered a stroke and so there isn't a stroke to be counted.
Can't think what Foxholer has in mind re outside influences.
In match play, when your opponent has picked themself up off the ground after rolling around laughing after your airswing and cancels your stroke because you played out of order. Why would your opponent do that? So you could do it again to further the entertainment and humiliation.