Sounds like it could be a MAF issue, If the ECU is seeing too much or not enough air and dropping AFR to 11 and bouncing around under WOT then there's definitely something going on with that tune or your MAF. You can try Cleaning your MAF with some MAF cleaner, Be really careful not to handle it by anything other than the connector and be sure it s completely air dried before re-installing. If that doesn't fix the issue then my guess is that the previous owner added or swapped parts without the tune and just drove it like that. Ive seen too many drivers with "performance" parts with not tune making the rest of the tuning community look bad. Your tuner should be able to load on a limp home tune just to test for other issues and while its there they can do a dyno tune and get you running with the full potential of those parts.
13 WRX Hatch - Cobb OTS Stage 1