Does cooking non-halal meat with other foods render all of them non-halal, and is a small amount of fat formed from this meat excused to alleviate hardship? And is it a condition to have a strong presumption that the slaughterer is Muslim or from the People of the Book for the slaughter to be considered halal?

What is slaughtered by a non-Muslim or a Person of the Book is not permissible, and it is not allowed to eat anything from it. Everything cooked with it becomes like it. It is not permissible to use the utensils before washing them. There must be certainty or a strong presumption that the slaughterer is someone whose slaughter is permissible, because the default status of a slaughtered animal is that it is not ritually slaughtered (not dhakāh), and in case of doubt, the default applies, which is the impermissibility of the slaughtered animal. However, meats sold in countries where the majority are those whose slaughter is permissible are considered ritually slaughtered, based on the prevalent custom.