That's a challenging, diverse set of questions.
1. The electrons in the particular galvanic cell you mention join up with Cu++
ions from the solution to make plain Cu atoms, which sit on the Cu electrode.
2. Electrons, like all small things, are indeed fuzzed-out waves, not located in one exact place. The picture of them always hopping around, as if they were first somewhere then somewhere else, is not correct for electrons that have settled in to wave patterns in atoms. However, (and this should admittedly sound strange before you learn a little quantum mechanics) even in those stable patterns the electrons have some kinetic energy. More importantly, whether classical or quantum, energy is conserved. It doesn't disappear. The large-scale organized forms of it gradually trickle away into smaller-scale forms, allowing a great diversity of possible states. (That's the implication of second law of thermodynamics.) Anyway, all this energy has been around since the Big Bang, as you supposed.
The electron spin is something else, a part of what makes something an electron, and it persists undiminished unless the electron is annihilated.
3. No, electrons are really all the same sort of thing. That's not just a philosophical statement. Electrons are a type of particle called "fermions", for which no two identical particles can have exactly the same quantum state. If you pick some spatial wave pattern, it can only have two electrons in it- one for each distinct spin state. That has enormous consequences. For example, it's the only reason that all the electrons in an atom don't pile up in a boring low-energy ball near the nucleus, so it accounts for all of chemistry and hence life.
(published on 05/07/11)