What is the importance of the solution in an electrochemical cell?

[stfz]

I'm wondering about the importance of the electrolytic solution in an electrochemical cell.
For example, we have Zn/ZnSO4 and Cu/CuSO4.
According to the electrochemical series, Zn will reduce Cu, and we will have a reaction.
Zn(s) -> Zn2+(aq), Cu2+(aq) -> Cu(s).
So there MUST be Cu2+ in the solution. But what about the electrode? If I had an Ag electrode in a copper solution, would the reaction proceed? (I am told it will not... but why?) The same net reaction would take place - Zn reducing Cu in solution, causing Cu to plate onto Ag. The only difference is that the electrode carrying electrons is now Ag.
Similarly, if I had a Ag/AgNO3 solution and a Cu/Zn(NO3)2 solution, would Cu displace Ag in solution still? I mean, Cu oxidize to Cu2+ and enter solution even if there is Zn(NO3)2?
Somewhat confused :P
Help would be appreciated :)

 

[Borek]

If I had an Ag electrode in a copper solution, would the reaction proceed?

Yes. Electrode can be inert in this case - besides, once few first copper atoms get reduced, you are back at a square one, copper electrode and copper in the solution.

Similarly, if I had a Ag/AgNO3 solution and a Cu/Zn(NO3)2 solution, would Cu displace Ag in solution still?

Yes, Zn²⁺ would be just a spectator.

2Ag⁺ + Cu -> 2Ag + Cu²⁺