x2 n BiGMaC's suggestions. How many miles?
Time to get the car up on ramps or a lift, I think. If there IS something wrong with the fuel system, the usual culprit has been leaky injectors. Doesn't seem like it in this case, could be leaning out at WOT, so avoid WOT till further notice. More likely it is carbon buildup on the valves. Check:
The CAC for oil
The intake piping for oil
Turbos for carbon buildup & oil
Breaks/tears in turbo piping
You may have an aftermarket catback installed, something like a Borla or a Corsa, but the mufflers &/or tips would be stamped accordingly, IME. Aftermarket downpipes can also make the tone deeper.
As far as tuned/stock goes, you have to get the strategy code (using a tuning device) and load a stock file to start with a clean slate. Unless you can track down the previous owner and find out from them. Or have the latest PCM calibration installed by dealership (may not be the wisest decision on multiple levels).