the gas stovetop answer on the site paskened that lighting a gas stove on yom tov is fine, a candle or pilot light is best but the regular igniter also works. following up on what is still not clear.

1. everyone talks about needing an existing flame on yom tov. what exactly does that mean and why does it matter, since the answer allowed even the igniter? is the existing flame idea a chumra, a preference, or the actual din?

2. why do many people leave the stove or a burner on for the entire yom tov? is that a halachic need, a minhag, or just convenience? and if the flame goes out, what changes?

3. on shabbos the toaster thread paskened through bishul and yad soledes bo. but on yom tov cooking is mutar, so can a person use an electric toaster, an electric kettle, or an induction cooktop on yom tov? is the question then only about the electricity itself, and how does that work differently on yom tov than on shabbos?

4. and the adjustments: raising or lowering the flame on yom tov, turning a burner off when the food is done, putting food back on a warm stove. which of these are mutar and which cross into hadlaka or kibuy?

bottom line: what are the actual rules of cooking on yom tov, and which parts are just custom?