[Coda]

One electron is one unit is exactly it -- it's as fundamental of a measurement as you can get, nothing arbitrary about it.

Stored-up electrical energy, not mechanical energy. It's possible to CONVERT between the two; that phenomenon is called "magnetism."

It's potential because it's not moving -- it CAN move, if it's allowed to. Just like a ball sitting on a table isn't moving, but it has potential energy: if you pull the table out from under it, that energy turns into kinetic energy.

A potato battery has measurable voltage because the metals you put in it have different electric potentials -- that is, given an opportunity, the electrons will move from one piece of metal to the other. And connecting a wire (or a multimeter!) between those pieces of metal provides that opportunity. It's like falling off a table; the electrons would much rather be on the lower-potential piece of metal than the higher-potential one.

Without going into too much detail right now because I'm tired... Charging a rechargeable battery is like rolling a boulder up a hill -- you put energy in, and later on, that energy can come back out.