I will use pliers to apply a sharp bend at the point where I'm going to cut the excess, just to make sure the core doesn't wander. Once the string is wrapped on the peg, the core should get locked in anyway.
I never wrap any turns on the post by hand, as this could introduce twist. I just keep tension on the string as I turn the tuning key to take up the slack, and make sure the wraps are tight.
Theoretically, tuning the string to a higher pitch (tone or semi-tone) and leaving it sit for a few minutes should do exactly the same thing as pulling on the strings laterally (bending or pulling). If you bend or pull excessively just to stretch the strings, you're putting force on the nut and saddles at unnatural angles, which could cause some undesirable wear over years of use.
The pitch of a given string is a factor of the length of the string, and the tension on it. Stretching a string just means temporarily increasing the tension so that it settles into a new natural length. Tuning it and leaving it for a little while should achieve this. Over tuning it will achieve this faster because of the increased tension.
If you make sure the string is not binding or twisting anywhere as you install it (at the post, nut, saddle, or bridge), you should end up with a string made up of several straight sections: post to nut, nut to saddle, and saddle to bridge. The use of "witness points" just pays attention to possible binding points, because there should be no kinks or bends anywhere in the string once it's under tension.
