A pinging or popping sound coming from the duct work can come from thermal expansion—the ductwork expanding and contracting as it heats and cools. Or, air blowing past a loose flap of metal can make the sound. Track along the duct runs, listening for the sound. If you locate it, make a small dent in the sheet metal to provide a more rigid surface that’s less likely to move as it heats and cools.
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.