If the car backfires, that means gas is exploding in the exhaust manifold and not in the cylinder where it belongs. If it's kind of clunking that's probably an engine miss.
That plus a code for a large leak says you have a large vacuum leak. The vacuum leak throws off your fuel/air mix, makes it impossible to burn completely. Your car's computer is trying to compensate, but it's relying on bad information. This can get your fuel/air mix even further off, which is why you have a miss and sometimes backfire.
Most likely a vacuum hose is off somewhere, or split open, or the intake manifold gasket has blown. If you look under the hood with the engine running, you can probably hear a hissing noise. A piece of hose in your ear can help you find where it's coming from. Find the leak, fix the leak, and you're on your way.
PCV valve gone bad, probably not. PCV valve broken off or completely missing, possibly. PCV hose ruptured is more likely.