Hi.
I'm here on my second-and-a-half trip. I'd definitely say most is off-road. Yes, there are a few stretches where you're on asphalt for a fair distance. But overall, it's very minimal.
Re: elevation gain, I'd say it's not a big deal if you're in relatively decent shape. Yes, some parts are quite steep. But over the entire 1000 km, it's not a big %. Overall, it's rolling hills, though. You're not walking on flat paths. And there are plenty of rocky sections, so a stroller would be a hassle.
Don't do the stove. Not necessary.
I've only walked at dusk or night a few times. I much prefer daylight, simply because I like to see the scenery -- overall it's quite beautiful. And in some stretches, you could get injured if you stumbled in the dark. But I think this depends on personal preference. One note: a local farmer told me on this trip that too many peregrinos walk in the early morning. While they often have head lamps or reflective clothing, he said it's still hard to see them. He was worried. I met him on a pretty rural/remote section. Just something to keep in mind if you prefer to walk in the dark a lot. (Meaning -- light yourself up like a Christmas tree!)
Melanie