Thanks for that! it cleared up a lot of my thoughts
But regarding question 1, what did you mean by flow of charge? It just got me thinking that in the situation where Cu2+ is freefloating in the solution, it would actuallly start getting reduced at the cathode instead of zinc (or react directly with zinc itself).
I would redirect you to my 'Some thoughts on electrochemical cells' post here
http://www.atarnotes.com/forum/index.php?topic=148802.0Without shamelessly advertising myself, it's a summary of a few misconceptions of electrolytic cells.
So, what part of that is useful here? We have an electrolytic cell with copper and zinc. Evidently, the zinc electrode is lower on the electrochemical series and thus is the negative electrode, while the copper electrode is the positive electrode. For electrolysis to work, we have to connect the negative electrode of an external battery (with bigger voltage than produced by the cell) to the copper electrode and the positive electrode to the zinc electrode; positive to negative.
Now, the tendency for zinc metal to react with copper ions can be thought of as a voltage, as it releases energy per electron transferred in the reaction. However, the external battery provides a bigger voltage that overrides the intrinsic tendency for copper ions to react with zinc metal, and FORCES the charge to go the other way (i.e. forces the reaction between copper metal and zinc ions to force the electrons to move from copper to zinc, or positive to negative).
Why is it that the hydronium ion and hydroxide ion concentration decrease as the other increases? My understanding is that although at 25 C, the pH would be 7, I would expect that the hydronium ion concentration remains constant with the hydroxide ions. However, this is not the case. Why is this so? I mean why does the concentration of each not stay the same?
Intuitively, it makes sense that the protons would transfer from the acid to the water, eg HCl, increasing the overall concentration of H30+ ions and thus decreasing pH. However, what I am really asking is what would occur if a base was present and if there was just water?
Any help is appreciated. 
Protons and hydroxide ions are in equilibrium with liquid water. If you add base, the base reacts with the protons and decreases the proton concentration, so by Le Chatelier, the system will attempt to compensate for the reduction in proton concentration by decomposing more water to replenish the proton concentration. This ends up increasing the hydroxide ion concentration.
Alternatively, look at the expression for the equilibrium constant for water.