1.  I see nothing wrong with that. Neutralization reaction.
2.  Sounds good.  With out looking at any texts.

3.  Like a little more to go on. But
If it is at the anode. Think of it like this electrons flow from the anode (-) to the cathode(+)
So H₂ = H+ + 1e  The electron is released at the anode and is consumed at the cathode.

4.  No if the reading is negative.  Turn your meter around.  For example if you put a volt meter on a cell and it reads 1.1v then taking the volt meter and switching the wires you will get a -1.1volt reading.  

2.  quantum theory: http://antoine.frostburg.edu/chem/senese/101/quantum/index.shtml
     Here is a link to some infromation regarding Quantum theory.  Quantum theory is a very large topic.  Particle/wave nature is one aspect of it.  This is most likely what your instructor is looking for.

3.  The aswer to number three is it can be.  It depends what is on the other side of the cell.  Are you oxidizing or reducing.   But in "a standard Hydrogen half cell"   Hydrogen gas is being used
H2 = 2 e + 2 H+ . . . . anode (oxidation) reaction
Zn2+ + 2 e = Zn . . . . cathode (reduction) reaction

Are there many reactions that will produce hydrogen gas.  Yes.  In this case H+ is accepting the electrons or being reduced.  Either a strong oxidizer is needed or an electrical sorce like a battery or something.  
Example:  Zn + HCl = ZnCl2 + H2  
              Zn = Zn2+ + 2 e-
              2H+ + 2e- =  H2
But this would not be considered a standard hydrogen half cell.  (meaning half of the cell is not composed of a hydrogen gas component)


4.   Yes.  regardless of what color the wire is.  Red or black or green.... if there is a -/+ voltage.  Definately.