meh

False.

There are various ways to hang a man. Usually the goal is to break the neck, to minimize suffering, but not always (look at how the savages in Iran hang homosexuals - raised slowly off the ground suspended from cranes - to maximize suffering). Regardless, that has nothing to do with the knot and all to do with how far the drop is.

The knot must be a slip knot so that the person being hanged does not slip out from the noose. A proper Hangman's Knot (or Hangman's Noose) tightens around the neck as the rope becomes taught, and spreads the forces thruout the knot to lessen the chance of the rope breaking.

Look at any real hanging (there are videos), it is always a slipknot of some sort.