This is an indication that your Friedrich PTAC needs a professional cleaning. If you don't follow the schedule for regular maintenance as suggested in your manual, moisture can build up in the base pan inside the PTAC, and mold and mildew can grow in the water and fly out as black particles when the unit is on. Contact an authorized Friedrich dealer to have a technician clean your PTAC.
Heat pumps are designed to cool and heat. Simply put, in the winter the pump blows warm air into the room, and in the summer it extracts warm air out of the room. So adding a heat pump alone would be like having two air conditioners and one heater. However, if you really want a heating option, upgrade your current PTAC to one that heats and cools. Most combination heating and cooling models perform best in milder climates where the temperature does not drop below 45 degrees Fahrenheit.
Snow and rain will not hurt your Friedrich PTAC. The elements that are exposed to the outside are sealed during the manufacturing process to protect them from moisture. What you should do is drain the pan at the end of the season to prevent it from building up moisture. If you drain the pan and remove the sleeve (the metal unit that holds the PTAC in place), you can use a cover.
This can be an indication that you don't have the right size PTAC for your room. Consequently, your PTAC is "short cycling," which can happen if the unit is too large for the room. Cool air bounces back from a wall to the thermostat, giving the thermostat a false reading and the unit turns off. After a few minutes, the thermostat picks up that the room is warm, and it tells the unit to turn back on. Contact your dealer to explore whether you need a different size Friedrich PTAC.