Does the photoelectric effect occur while heating food on a metal plate in a microwave oven? If not, then why doesn't it occur?
No, the photoelectric effect does not occur in a microwave oven.
The workfunction for a metal is the minimum photon energy required to eject an electron from the metal via the photoelectric effect. Workfunctions are typically in the range of several electron volts (eV). Potassium, for example, has a workfunction around 2 eV, see here for a list..
The energy in a microwave photon can range from 0.00001 to 0.001 eV; much to low to eject an electron from a metal.
For more background on the photoelectric effect see this earlier SE Chem Q&A