Yes, one piece of Koa from head to heel. It is a fun shape to carve.
Vertical head stocks work very well, but seem a bit weird the first time you use one. If you don't fancy carving the whole neck in one piece, I can recommend a two piece solution. Just a slot in each piece, and the resulting joint is very strong and stable.
This is the first one I made, back in 2009. I decided to use a zero fret and to do without a nut. The construction is self explanatory.
John ColterView attachment 125380
That would totally freak me out. You are right about tuning....you crank the tuner on one side of the head and a string on the opposite side tunes up.