Yes, I know it's not technically just methane, but methane is its primary constituent.
"Fossil gas" is also probably a suitable term, but I like "fossil methane" because it gets that spooky chemical name benefit.
Yeah they can and they do lol. I just fried some liver on a glass top, can't tell it turns on and off. The liver fried steady. Back when I had coil I didn't even know that it turned on and off. That how little it makes a difference: I can't even tell without being informed about it academically.