your questions 1 and 3 are roughly the same issue, and here’s your answer:
for a battery, there’s a salt bridge between the anode and cathode that fixes for the electron-loss you’re talking about, to put it in your words.
Most little batteries acualy arent designed with a salt bridge, but the cathode, or is it anode? doesn’t get used up, it’s a piece of carbon. Feh… did you learn about batteries in high school yet? They go over all that stuff. Look it up online, you’ll see diagrams, and it’ll show all the ion exchanges at all the relative points.
For generator-produced electricity (like on the grid, you know, in your house), the voltage or electromotive force (emf), is produced mechanically by moving wire loops through magnets, which induces a an electric field and thus a voltage that pushes a current in the wires. The elctrons just go in a full loop.
as per your question 2, you’re taking vague descriptions on what we sort of know about subatomic particles and applying it weirdly using classical mechanics. Nobody “decided” to move electrons instead of photons. The phenomena of the battery and Faraday’s principle (generators) were all discovered independently before the later subatomic explanations of photons, electrons, protons, neutrons, and even ions, etc. All these explanations came later to describe all the phenomena we had discovered in physics. But even now, our “knowledge” is really fuzzy on these particles; the experiments we can perform show wackadoodle behavior from all these particles, showing they also act like waves, and quantum mechanics lets us make predictions in certain experiments, but also fails to give any description as to what’s going on between electrons and their nuclei they’re “orbiting”. Are they orbiting? If they are, why aren’t they radiating? etc.
What you need to know is that this dude once stacked nickel, copper, and cardboard soaked in vinegar, and thus invented the battery. And then later another dude noticed a compass getting deflected by a current, and then we ll figured out that a changing electric or magnetic field induces the other kind of field at a right angle, and then somebody was like “hey, let’s spin wires around next to magnets, and wel’ll be able to get elctricity!” and then provided power from a source other than a battery was born.
From there, the thing to remember is that The reactions that occur in the battery are well described by physics and the equations balance, and you can learn them, and so are the equations that can tell you how strong a generator design will be.
That’s what you need to remember, and learn if you haven’t yet