Check and replace the two or three vacuum lines. One goes to the fuel pressure regulator and the other goes to something on the manifold by the top of the valve cover. Both connect under the manifold pretty much as close to the driver side bottom of the manifold as possible. You should be able to feel them if you stick your hand under there.
Get a valve adjustment or do it yourself. Run some injection cleaner through the tank. Use about two or three times regular strengh. In other words, two or three bottles with 1/2 tank of gas. Change the oil after you do this with 10-40 winter in Canada, 20-50 summer.
For the other vibration, it could well be your drive shaft. You should check the bushings on the upper control arms (thrust arms) and replace if necessary. HAVE YOUR TIRES CHECKED AND BALANCED. Many times it is tire related. Rotate them when you do this as it may make a difference too.
Hope this helps and good luck. You seem to have stumbled on one of the worlds finest sedans and taken care of it will reward you well.
Mike Holbrook
Meridian, Idaho
1992 535im, 17", Euro M5 Throwing Stars 8's & 9's, FK-451 235/45s & 255/40s, M5 Sway Bars 25/20, Conforti chip, Lowes Ram Air, glass sunroof