Shofar and trumpets are a Tanaic dispute for muktzeh on Shabbos. One important variable is that a shofar is curved and usable as a cup for a child. R yehudas position is that the shofar is not muktzeh at all but the trumpets are. R shimon holds even the trumpets are not muktzeh (evidently he holds a utensil primarily used for issur is not muktzeh) R Nechemiah holds even a shofar is muktzeh bc he holds utensils can only be used for their primary use on Shabbos

The terms shofar and chatzarzros for confusing and can be used interchangeably. The gemara lists other examples or such phenomenons.

A stovetop can have food on it before Shabbos if the stove is fueled with straw or stubble. These materials wouldn’t really heat up food anyway so there’s no concerns. However, good fuel like wood is forbidden to fuel the stovetop for food on Shabbos with food on it (we’re scared the fuel may be stoked to expedite the cooking process.)

This prohibition of having food exposed on fuel on Shabbos is a dispute between chananya and the rabbis. Acc to the rabbis it is always forbidden if the food can use some xtra cooking, but acc to chananya is it ok if the food has reached בן דרוסאי- barely edible. The gemara is unsure whose opinion is reflected in the mishna.

One can shovel away the coals or put ash on them and then keep cooking food on the stovetop on Shabbos. Acc to beis Shammai this is only for hot water but acc to beis Hillel it is permissible to do this for food as well.

One cannot our food on a stovetop on Shabbos bc it looks like cooking. This is even if the fire if the fuel is covered with ash. But acc to beis Hillel, one can “return” food to a fire on Shabbos.