Essentially does the component of a microwave which generates those microwave photons operate using an AC power supply connected to a broken circuit which causes an oscillating dipole to radiate electromagnetic radiation? Is there any amplification that is needed?
it has an AC power supply connected to an unbroken (not sure what you mean by "broken") circuit called a microwave oscillator. At the frequencies generated by that circuit, the dipole antenna it feeds looks like a piece of hollow pipe with a flared-out end on it, pointing into the oven chamber.
The necessary amplification is generated by the vacuum tube (called a magnetron) in the circuit that also does the oscillating.
The basic physics is the same as that in a lower-frequency radio transmitter, but the implementation details are different because of how high the operating frequency of the microwave tube is.