One is not allowed to keep food that is still cooking when Shabbos begins on the fire (bc they may come to stoke the coals). However, once the food has reached בן דרוסאי- edible state, it is permitted (bc it’s less likely someone would stoke the coals). The equivalent with bread is if the bread turns crusty on its top that faces the fire it is ok to keep it on the fire. (R Eliezer requires it to be crusty on its bottom as well)

There’s a similar application of בן דרוסאי by בישול עכום. If a Jew cooks something to edible state, it is permitted to eat the food even if a non Jew finsihed the cooking.

By fires as well, one should not light a fire right b4 Shabbos and leave it by itself bc one may come to stoke the coals. But if the fire has already taken hold of “most” of it it ok. (There a dispute if that means each piece of wood must be mostly on fire or if the fire just needs to be sufficiently established)

A single piece of wood must have fire hold most of it to be left on b4 Shabbos. There’s a dispute if that is most of the thickness or most of the circumference.

Two anomalies where these rules don’t apply- by the Korban Pesach roasting it can be put on right b4 Shabbos bc the members of the group will remind one another and also the fire in the Temple lit to warm the Kohanim. (Bc kohanim are זריזים and would not stoke the coals)

Certain circumstances of reeds and date pits used as fuel for a fire do not require the fire to take hold on most of it b4 Shabbos bc they are easily combustible. Also pitch, sulfur, cheese, and grease.

The Rabbis forbid lighting candles on Shabbos with wicks that don’t draw the fuel well. Examples would be the wooly substance inside bark of cedar trees, flax who stems were beaten but not combed, floss silk, wooly substance under willow tree, green substance that grows on boats in the sea, wool or hair.