That should be a fret.
Its where the strings are stretched over from the tuning knobs. Its sometimes called the 'zero' fret.
The neck of a guitar as no other name than that -- the neck. This is the part of the guitar that connects the body to the head of the instrument. Located on the neck are the frets and the fretboard. In addition, all of the guitar strings rest slightly above the fretboard. In short, "the neck" is already a technical term. It doesn't have a special name to make it sound fancier.
Bottle neck, brass neck, guitar neck.
I'm not sure if this is what you were thinking of, but the Chapman Stick comes to mind.
a Guitar
You can purchase used electric guitar necks from ebay. You would have to search 'used electric guitar neck' and most likely the make of the guitar neck you are looking for.
The Mitchell MD100 guitar neck is glued to the body.
yes
Not really. I have a guitar and I don't get hurt from playing it. So no.
Taylor swift does :) she also has baby Taylor guitars for kids
no
The keyword "keys" on a guitar neck refer to the different positions where you can play a specific note or chord. These positions are determined by the placement of your fingers on the frets of the guitar neck.