How do I easily tell if vent below microwave is vented to the exterior?
Properly installed range hood vent, including those combined with microwaves, almost always use an external vent hood that has a flap to prevent backdrafts. The flap is pushed out by the increased air pressure created by the vent fan.

While there are sometimes internal backdraft flaps, there is almost always an external one as well.

Look at the exterior hood and have someone turn on the vent fan. You should see the flap moving. If it does not, you likely have a problem.

You can remove the external hood by removing mounting screws and cutting the caulk seal around the edges. You can then look into the hole to see where (if) it is connected.

Many vent hoods can be set up for interior or exterior venting. This usually involves changing the orientation of the fan itself during setup. The installer may have left the fan pushing the exhaust into the kitchen. If so, you should be able to feel a draft at the top of the unit when the fan is on.