Engine vibration is not normal. I'd check motor mounts. My E53 had a lot of vibration, and it turned out the oil-filled motor mounts had failed. PITA fix, but car ran much smoother. On the E53 the engine was also sitting and inch or so lower than it should with the failed mounts. Get a close look at them from above and below, and look for leaking oil. If the mounts are oil soaked, that may be your culprit.

Your car may also be misfiring at low RPM; there are a number of possibilities for this like bad coil packs or air leaks. If it gets bad enough, it will through a CEL and point you in the direction of the offending cylinder. As far as air leaks, if the car leaks oil at all, it is not properly sealed, and can cause these problems. But it does not have to be leaking oil to have an air/vacuum leak. If you have access to a smoke machine, this will tell you if everything is properly sealed. Plug the throttle body, and smoke it from the oil fill cap. I'd do the smoke test first, as you're not throwing parts at the car, and it's pretty minimal labor. Even if you get a "Misfire Cyl 6" type code, the cylinder/coilpack/spark plug could all be perfect, and you just have a vacuum leak.

As far as the ABS/DSC failure, I have not heard of the massive module failures as on the e53/e39 either, (I had to rebuild one of each), but it may just that the E70's aren't old enough yet. The E53 was particularly bad because the module location, (behind the driver's side headlight down low.) I'd try to get access to a good scan tool and see if you can access the module. If you can't talk to the module, I see no choice but to send it out to be rebuilt. If you CAN talk to the module, see what error code is at fault; ie. a faulty wheel speed sensor and address that. If you do end up sending it out, you will need to reprogram the module once its rebuilt.

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2014 BMW 328i Xdrive
2011 BMW 335i M-Sport
2008 BMW X5 4.8i Sport
2000 BMW 528i 5sp