Their purpose is to find out which knowledge can withstand critical questioning, and which crumbles away.
Asking questions are always good. But what purpose does it serve when they are aimed at not getting the knowledge but just to counter?
I don´t think that is correct, unless you use paranormal to indicate anything we don´t understand. Which would imply that black holes are paranormal, as are large parts of quantum physics. Things that are unexplained are simply that: unexplained. That doesn´t tell you anything about their nature.
If an experience or sighting cannot be explained with everyday science, it is paranormal.
Paranormal literally means ´outside the ordinary´. I think it is used to refer to phenomena that are supernatural: ghosts, clairvoyance, etc., things that lie outside the common everyday world and experience.