Welcome!
Lol Ithink you are off by a 0 on your rpm posts. our car idles at 900 rpms, so I think that you mean it fluctiates from there.
Good that the tb was replaced. There is a FAQ in one of the sticky's read through there, it will answer many of your questions.
A few things to watch for is, boost/vacuum leaks from TBB, fhose (for 00 model cars, the 01.5 did away with fhose), you can also get boost leaks from other area's as well. so it would be good to test it to make sure its good. Boost leaks will affect performance, plus can reduce life of your turbos. There are write ups how to check for boost leaks, search for those.
about your rough idle, somtimes the car will idle rough if it has a vacuum leak. It could be misfires as well.
If I were you i'd get the vag-com cable (ODB-II) and the vag-com program so you can check for codes yourself, it will really help to troubleshoot problems.
At least check it for codes, the MAF can go bad, egt sensors (you have 2) can go bad. Oxygen sensors can go bad (You have 4)
you want to make sure and fix the codes for it to run right, it will effect performance and cause larger problems in future if left unfixed.
The CEL light can come on frequently

But doesnt have to be constant problem once you get your codes all fixed. Is your CEL light on at all?
Well so many other things to say but biggest thing is it is such a love hate relationship. When its running great it can really put a smile on your face
if something breaks it could get real expensive in a hurry, plus there tends to be a lot of maintenance.
With that said, have fun
One more thing, I'd install a boost gauge if you dont have one already, it will help tons to watch what your boost is. stock runs around 9psi and if chipped will go anywhere from 14psi to 19 psi depending on your chip software you go with.
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