You can usually slip the belt on the motor’s (smaller) pulley first and then start it on the blower pulley. Rotate the blower pulley by hand, holding the belt in place but keeping your fingers from getting caught between the belt and the pulley. The belt should slip right into place. If it seems to be too tight or difficult to set in place, it may be necessary to adjust the motor mount to provide more slack.
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.