No one is complaining, and the comment about intentionally causing a short circuit was about as constructive as you are likely to get. Speaking as constructively as I can, if you had used that investigative technique in my house, I would throw you out and call my lawyer.
Now speaking as a forum Moderator, I must ask you to knock off the sarcasm. Everyone who comes here does so of their own free will; nobody gets paid to help anyone else. Most of the time, the membership will offer whatever help they can. But nobody is going to help you, if you are rude. Consider this a warning: be polite, or look elsewhere for help.
To answer your three questions:
Question 1.
The term PSCC does not mean anything to me. Using ?prospective? in this manner is not a standard way of describing short circuit currents. I do not know of any electronic measurement tool that can predict the amount of short circuit current available at any point in any distribution system.
If you directly short circuit the output terminals of a breaker, and it does not trip, the breaker is bad. But you don?t test the replacement by shorting it out.
It is possible for the available short circuit current to exceed the rating of a breaker. When that short circuit takes place, it is possible for the internal contacts to melt together, preventing the breaker from opening the circuit. However, the amount of short circuit current available in residential applications should never exceed that level.
Question 2:
If you put in a new breaker, you should not need to test it. But I do not understand the scenario you are trying to describe. You mention a melted plug, a ceiling fan, and a light. What happened in the first place? What did the HO tell you, when they called for your assistance?
Question 3:
A breaker will not trip on a current that is only slightly above its setpoint. A 20 amp breaker, for example, might be able to sustain a current of 22 amps forever, without tripping. So I must fall back on why you are expecting the breaker to trip? What has failed, what has been damaged, and what do you know about the circumstances?