The overall cell equation according to the diagram and the title is actually:
Zn (s) + Cu^2+(aq) -> Zn^2+(aq) + Cu(s)
What you have stated is the zinc half cell connected to the standard hydrogen half cell.
As for the other points in your questions, I am not sure.
As for pressure, I think (am very uncertain), that this would not alter the equilibrium constant (which determines how far a reaction proceeds). The increase in pressure usually pushes the reaction to side with lower number of molecules.
As for the acid and nitrate bits, this would probably affect the concnetrations of the ions in the half cells, by decreasing them, causing equilibrium shifts to the side to best counteract this change.
I'm not entirely sure on this, maybe someone can correct me if I'm wrong.
Luke