Heat and A/C not blowing correct temperatures or locations

When the weather was hot this past summer and I would turn the A/C on, sometimes nothing would come out of the vents, no A/C, no vent, nothing. Then, all of a sudden, the A/C would come on, but it would be out of the floor vents not the middle ones. I would hear a single "popping" sound in the dash and then the A/C would come out the middle vents like it was supposed to. Now as soon as the weather is cold, I'm having heat issues. When I first cranked the car this morning, the heat blew hot air, but immediately started blowing cool air, not cold like the A/C, just cool. I heard the thumping sound yesterday again when I cranked it. I had to get the heater core and water pump replaced about 6 months ago. I've been told about the blend doors. Is there a separate blend door for the temperature and a separate one for the location the air blows? Or could this be some other problem?