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.
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