A microwave and refrigerator can be on the same electrical circuit because the refrigerator will not be running all the time.
However if you have a larger microwave that draws more power then it might trip the circuit.
But I've had my microwave and refrigerator on the same circuit before in a mobile home and although the lights did dim some when the refrigerator came on and the microwave was in use it never tripped the breaker.
it's best to have the microwave and refrigerator on separate circuits but it's okay to have the microwave and refrigerator on their own circuits.
A permanently installed microwave though does require it's own dedicated hardwired circuit.
A countertop microwave does not require a dedicated circuit.
However it's best for the countertop microwave to have a dedicated circuit because the microwave uses quite a bit of power.
A microwave could dim lights or trip breakers if other appliances are on the same circuit.
I have a dedicated circuit in my kitchen for my microwave which is much better.
A countertop microwave should easily be able to run on a 15 amp circuit.
I lived in a mobile home that had 15 amp electrical circuits in the kitchen and I ran my countertop microwave on the 15 amp circuit just fine.
Although having a 20 amp electrical circuit would be much better but a 15 amp electrical circuit will be good enough to handle the microwave.
But if possible it's best to have a dedicated 20 amp circuit to handle the power of the microwave without dimming lights.
I now live in a regular home that has 20 amp circuits and a dedicated 20 amp electrical outlet in the kitchen for the microwave.
It's much better that way but you can run the microwave on the non dedicated circuit whether a 15 amp circuit or 20 amp circuit.