None that requires the house electricity. Piezo, batteries easily work.

Not if it’s a tank system. They can, but they don’t have to, since the pilot stays lit all the time. A tankless system has to use some power since it cycles every time you use it.

My gas hot water heater does not have an electric start.

Some use a 9v battery on their starter.

Regardless, you can just use a match if you want to.

In either case, they don’t require mains power.

(Sure, there are different models, etc. but it’s not a requirement that all have an electric start, or a mains electric start)