My microwave has a time delay of 23 hours 59 minutes and the courtesy light only operates when food is being cooked. Am I permitted to put food into the microwave before/during Shabbat or Festivals for the heating/cooking to take place according to the time delay which has been set before the commencement of Shabbat/Festival? Does the food have to be ’solid’ or may one heat/cook liquids or a mixture of the two?

HaRav Moshe Feinstein writes (Shu"t Iggrot Moshe Orach Chayyim III 52)that cooking in a microwave oven on shabbat is a Torah violation. It would be forbidden therefore to put food in a microwave on shabbat that would be cooked later on shabbat on a timer. Even placing it in the oven before shabbat would be problematic because of the rabbinical injunction against leaving uncooked food on a fire (Chazon Ish Orach Chayyim 38 2) and the comparison made by some betweeen the microwave and a regular electric fire (Shu"t Shevet Halevi 8 185). One is permitted to cook food on a festival that is not shabbat. It would be permitted therefore to put even on the festival itself, uncooked food into the microwave- or into any other oven operating on a timer set before the festival.