You keep using that word. I do not think it means what you think it means.
Ahhh....my misspent youth...
1. Do pillboxes create a second location in a hex?
2. Does a unit that is moving through a hex with a pillbox have to pay the -3 cost of movement if the pillbox is in open ground and it elects not to use it? How about the -2 penalty for Foxholes?
I'm not sure what you are asking here. What penalty for movement?
3. Section 54.1 of the rulebook states that "When moving into and out of a hex with a Foxhole, units do not get the benefit of the Foxhole and maybe considered moving in Open Ground."
What this is saying is that when moving into the hex, you are not yet considered in the foxhole, so you do not get the terrain benefit of the foxhole until you end your move.
The only situation I can think of where a unit "moves out of" a hex is if it starts its movement already in a Pillbox adjacent to an enemy unit and attempts to move into the enemy's hex, at which point it is subject to Op Fire/FOF in its original hex.
That is correct.
4. Are there any restrictions as to where a Foxhole or Pillbox may be placed?
Not in buildings, bridges, or water. Sometimes other spots by scenario rules.