A microwave that runs but stays cold is a high voltage fault, and that is not a part anyone should be poking at with the cabinet open.

The turntable turns, the light is on, the fan runs, and nothing gets warm. That is the magnetron, the high voltage diode, the capacitor or the door interlock circuit. All four sit behind a capacitor that holds a lethal charge long after the unit is unplugged, which is why this is the one appliance where we ask people not to open the case.
On over-the-range and built-in units the repair is usually worth it. On a countertop unit under $200 it usually is not, and we will say that on the phone rather than after a visit.
Sparking inside the cavity is normally the waveguide cover, a small mica panel on the side wall that has burned through. It is an inexpensive part and a fast job. Sparking with metal trim or a damaged cavity wall is a different conversation.
A microwave that does nothing at all when the door is closed is often a failed door interlock switch. Three of them work in sequence, and when one goes out of adjustment the unit refuses to start on purpose.
Usually yes, because the replacement has to fit the same cabinet cutout and trim kit, and that combination is often expensive or discontinued.
No. Stop using it, and unplug it if you can reach the cord safely.