Your furnace's flame sensor is essentially a safety mechanism. As a thin metallic rod in front of the flame inside the unit, it's sole purpose is to confirm that your gas valves only open when a flame actually exists to burn that gas. When the flame sensor stop working, on the other hand, gas leaks can occur. To repair your furnace's flame sensor, expect to spend between $80 and $250. Even a full replacement of this part typically does not go above that range.
Put simply, any home that uses air pushed through ductwork for heating purposes takes advantage of forced air heating. In other words, this term refers not to your furnace, but to the delivery method of the heat throughout your home. Forced air heating is possible with electric or gas furnaces, or a heat pump. Any issues with this delivery system that aren't directly related to the furnace likely have to do with the duct work, which costs between $35 and $55 per linear square foot to repair, or the air handling unit.
Yes. You should expect to pay a diagnostic fee to cover the cost of the technician's visit, the diagnosis of your air conditioner's problem, and a quote for the repair options. You will be advised of the issue along with recommended options to correct it, which may include a system replacement if your unit is old or significantly damaged. If you decide to replace the system, the diagnostic fee will be credited toward your replacement purchase.