What you're describing about the shake is surging. Either get off the gas and go back at it, or just gun through it. The pedal is really sensitive sometimes so when you first gas it, your foot starts to oscillate a bit and that's what you're describing.
2011 e92 JzB 6MT
Akrapovic Evolution, ESS Tune, UUC SSK w/ DSSR, Stoptech SS brake lines, Eibach springs, OEM gloss black kidney grills, keyhole delete, LUX H8 3.0, full front clear bra, 20% tint, Macht Schenll Stud Conversion, Apex ARC-8 18x9.5/10 w/ 265/35 & 285/30 AD08's