[jblackburn]

Both issues (this and shutting off with AC on) sound like your PCV disc in the valve cover has ruptured.

You DO NOT need one of the PCV fix kits the 1.4T cars do, but the diaphragm built into the valve cover just needs to be replaced.

Usually accompanied by a P0171, P1101, occasional P0106, and whistling/honking noise from the top of the valve cover.

 

[jblackburn]

That...sounds terrible. More going on there than just this.

I hear a distinct vacuum leak though.

Scan the codes and check for obvious vacuum hose leaks or see if the noise is coming from the spark plug cover area.