Yes, but because electricity is mostly produced by gas turbines, and you could say oil & gas companies do rule the world. Utilities mostly take care of the distribution, and are naturally monopolic/oligopolic businesses which is why in most countries, they are regulated (or owned) by the state.
No idea honestly, but the main reason the battery lasts so long is that it turns the WiFi off, which is why I had to install Insomnia. It was doing fine so far, with 60% battery, but decided to plug it in since it's getting many requests now
I keep mine unplugged and it gets surprising good battery life, and I think it kinda improved with the downgrade. On normal use I would get like 8-10 hrs screen on time. No spicy pillow yet, though I did have that issue with my old iPod.
I'm with you here. I think Apple should let you install whatever OS you want in the device after the support cycle ended. But that's not gonna happen any time soon. Until then, we jailbreak.