[Coda]

Earth has a net neutral electric charge. But you can induce a charge in an object by bringing another charged object near it; it'll push matching charges away and pull opposing charges near -- electrons are very, very mobile little things and it really doesn't take a whole lot to move them around. So there's a positively charged region that's formed below the cloud.

You're completely correct about the motion of lightning. Note, of course, that it's (ionized) air itself that ends up conducting the electricity, so the path of least resistance might not be the shortest STRAIGHT-LINE path.

If you had copper and zinc, it would be a bad idea to stick it into an outlet, but not because it would form a battery... it would be a bad idea because you would be creating a path of least resistance between the two sides of the power outlet and that much energy flowing through a couple tiny bits of metal will start a fire. The fact that they're different metals is irrelevant there.

You're remembering the chemistry relatively well there. All consistent!

And yes, the electron literally does get displaced from where it was. It sticks mostly close to the surface, skidding across to other atoms, pulled towards positively-charged things. It doesn't go flying off the surface -- that would be a beta ray, and that takes a lot more energy.