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lol. it could be an engine mount mine has a knocking noise, shakes like a cam has been put in it. but it has idling issues but it doesn't not sound like a WRX, have you checked spark plugs, leads and coil packs?
it could be timing, i would also check the CV Joints and rear axles, along with suspension components to make sure they are all in good condition.
I thought the problem was sorted...it's not, but I think it may be that the timing is out. I mean it is out a bit for sure coz car is backfiring, but I dunno. either way at the moment it sounds like a WRX when accelerating and like it has a worked camshaft when idle, and it's pulling and shaking from the back end....it looks spectacular when it heats up and you just sit there idling...I wish the car did it for a good reason...I want a cam put in lol