What causes my heater to quit heating

The heating element is shorting out and causing it to blow the fuse

The problem is that heater fan motor. They are prone to failure when the brushes in the motor wear down. Replace it, they are about 100 USD

Maybe your fan motor has quit working ,but first check your fuses

the heater coil is blocked up or hose is frozen

Your blower fan is most likely failing. It sounds like it is rubbing on the cage, which causes the motor to heat up and quit functioning. Once the motor cools down it will operate again. You will need to replace the blower motor and fan assembly.

Your friend is right. To answer your other question these are two totally seperate fans but that does not mean that one fans fuse or relay did not affect the other. You should check your fuses and which ones, if any, are blown. It is likely that during your radio installation a bare contact touched something and blew the fuse(s). If the fuse is blown and, when you replace it and work your heater fan, it blows again then chances are your radio may have cut a wire upon sliding it in. Reply back to this post and let me know.

sounds like a fuse to me. hope so.

heater core may be clogged. disconnect the hoses. CUT THEM OFF THE HEATER CORE!!!! If you pull them you may damage the solder joints at the tubes causing a leak. Them connect a garden hose and flush one way then another till water runs clear.

There are 3 possibilities beginning with the most likely problem

1) If your heater heats up for a few minutes and then quits, chances are there is a blockage in the air flow, check for dust and grime blocking the air intake coarse filter , airgun blow to clear accumulated dust and otherwise clean the coarse filter .
2) If the heater fan blows but there is no warm air, the heating element needs renewal ( this happens very rarely)
3)If the fan stalls and the heater heats up and the thermostat kicks in, then this will be not be a DIY job. This is least likely as you said the air cooler works.