BMW Repair: mild to moderate vibrations at varying speeds, 2001 bmw 325xi, bmw 325xi

Question
HI, The car is a 2001 BMW 325xi with the sport package Manual shift with 5 speed gearbox. Just to start, I was a mechanic for about 6 years. I havent turned a wrench in about ten but I do have fairly strong mechanical ability/aptitude. That said I'm completely in foreign territory with BMW. (no pun intended).  So, I just bought the car about a month ago. When I bought it it had a mild vibration coming from the back, felt like a tire slightly out of balance. I had the tires balanced and set all air pressures according to the door sticker. 38 f / 45 r . The vibration was good for that day. Next morning (cold out) vibration was back and the traction light flashes a couple time around turns. (I was definately driving fast and that could have been normal at this point.)This happened last wed. I drove the car about 700mi on Thursday (Thanksgiving) and towards the end of the trip the vibrations were fairly bad. Not dangerous bad but I would not have purchased the car if it were vibrating like that bad. The vibrations seem to be occurring between 45 and 75mph, then go away until about 100 then they are very mild. Today the engine cut out or lost power 3 times on my way to work (like the fuel pump cut out)very briefly and then kicked right back in and on my way home when in second gear (very mild acceleration) the engine cut out again and the traction light flashed briefly. The car had definately not lost traction. No gravel or anything. During this whole experience the BRAKE light has been coming on in yellow intermittently and every time it comes on the engine kind of loses power briefly. The car has had a new front diff put in, new front axles, water pump and tensioner. both front lower controll arms have been done, a new battery and the tires are new. also the rear brakes are ok and the front ones are low but the pad sensor has been taken out and looped through the bleeder valve rubber cap. (not my handiwork). I have heard about the drive axles possibly being a problem but none of the boots are ripped and the front ones are new. I'm terrified that the car has a transfer case problem because the vibrations seem to shift from the rear to te front and become much more pronounced on the left side when making right turns. Sorry I wrote so much but really need help. Thank you. Sean.

Answer
There are a couple of things that you did that I would change.First would be the air pressure,I would set them both at 36 psi max.Having them different maybe causing the abs/asc from working correctly.Having the front pads being low enough as to removing the wear sensor is also am issue that should be looked at,the pads being that worn the rotors too must also be worn.Check the fluids in the transfer case and the front /rear diffs.Having the correct fluid is essential in the "xi" models.All three I belive are different fluids.Check the front wheel bearing on the left side it may depending on the mileage of the car be worn.Checking all the bushings for any cracks(ie the center bearing as well hard to see but may have a broken mount)