Foul tip caught, foul ball, or out?

[DG]

I based my comment on the fact that the ball "becomes temporarily stuck behind the catcher's chest protector, then eventually falls out after about 3 full seconds, and the catcher catches it before it hits the ground." The catcher did not pull out a lodged ball, it just fell out. 3 seconds is a long time so I can see how an umpire would rule the ball is lodged, and therefore dead. But, I'm not aware of a time limit on a ball to be considered lodged so in the judgement of this umpire it wasn't if it fell out on it's own in 3 seconds.

What if a ball got by the catcher and stuck in the backstop fencing, and as the catcher went back to get it, but before he touched it, it fell to the ground?

What if a ball bounces under the catcher on a swinging 3rd strike, runs up the umpire's leg and hits him in the throat, underneath the extension on his mask, sticks there briefly and then drops to the ground when the umpire jerks his head back as he realizes he has been hit in the throat and the ball is still there?

What is the time limit on being lodged?