1.) if a battery weren't connected to an electrolytic cell, would the cell be spontaneous in the opposite direction? Yes. That's why the electrons don't travel to the cathode. They want to stay at the anode "spontaneously". We only say it is non-spontaneous because the electrons do not want to travel to the cathode. The traveling process is what creates energy/supplies energy. That's why a battery is always spontaneous. In a battery, the anode is the negative side and electrons want to spontaneously move to the cathode, which is the positive side. When this happens, it creates energy. That energy can be used for your car or whatever. But eventually, electrons that travel to the cathode side are not attracted to the positive cathode because the solution becomes more and more neutral. Remember, when metal ions accept electrons, they become solids. So the positive ions in solution at the cathode side are getting electrons and are adding to the cathode. This is called accretion (solid formation). This makes the solution look more "negative" (to be exact, it's making it more neutral but you get the point). At the anode side of a galvanic cell, the solid is dissolving because the electrons are leaving the solid, creating ions which go into solution. These positive ions also build up and electrons end up not wanting to leave the anode side because they are attracted to the positive ions in solution. All of this is happening, making the battery harder to work over time. That's why we have a salt bridge. The salt bridge adds Cl- to the anode side to keep the solution negative (unattractive to the electrons) and Na+ at the cathode side to keep it positive (attractive to the electrons).
2.) in the salt bridge, can the cations produced from the anode during oxidation travel through it (and vice versa at the cathode) or is it just the salt ions within the original salt bridge? The ions do not across. Only the electrons. The salt bridge ions also do not react in any way with the chemical process.
3.) what's the purpose of driving a non-spontaneous reaction in an electrolytic cell? is it to produce a certain kind of metal? i don't see why you couldn't produce the same product using a very strong reducing or oxidizing metal so it's a spontaneous process. Electrolytic cells are very important. Your laptop battery is an example of an electrolytic AND galvanic cell. If you think about it, electrolytic is like charging something. We are adding energy into a reaction so that it can go non-spontaneously because that non-spontaneous process creates energy for us later. When you plug your iPhone or galaxy 5S into the wall, the power is driving a non-spontaneous reaction. But when you unplug your phone, the reaction occurs spontaneously to cause electrons to travel. When all the electrons that can travel do, the battery dies. That's when you need to replug it.
So electrolytic is electrical (energy) to chemical. Galvanic is chemical to electrical (energy). It's a big cycle.
