I have just started getting the same issue with my 2007 cabriolet.
I installed a new MAF and the engine still “pulses” on cold idle and throws up the running lean issue. Exhaust starts popping and there is a “thud” sound from the air intake.
However, if i unplug the MAF, the car idles perfect and the pulsing, thuds and pops disappear????
At the moment I am running the car without the MAF plugged in until i can figure out why it doesn't work with a new MAF installed.
Would be interested to see how yours runs if you unplugged the MAF?
Following this tread to hopefully find some answers.