As for the wheel shaking it's your thrust arm bushings. Swap the whole thing then do an alignment. Make sure your mechaninc does a thorough inspection. Ofcourse you should also make sure your tires are in good shape as that could contribute to the shaking. If your shaking between certain speeds and while you are braking (if not now it will happen as it gets worse) then its the thrust arms.
Engine shaking, i would star off by cleaning the MAF sensor(CRC MAF cleaner from Napa Auto Parts), and throttle body. Also inspect spark plugs. If your MAF is dirty or on its way out it will casue all kinds of wierd symptoms. Why do you think sludge is the issue? If it is you could consider sea foam, but i suggest you read up on that first.
I thought you were gonna get the E39.