No, you suffer the CA change DRM. In the SK3 rulebook, 7.8 says once you fire a turret-mounted weapon other turret-mounted weapons suffer the same CA change DRM. The MPh and DFPh are counted as one phase for firing (otherwise you wouldn't be able to fire a MG in the MPh then fire something else in the DFPh per 7.8).
Yes, if it changes VCA to fire the BMG, both suffer the NT CA change DRM (+3/+1/+1). The TCA stays the same with respect to the VCA as you change VCA, so the TCA changes on the map, and you may have to change the TCA to fire the MA, which adds more DRMs.
The CA DRM no longer applies it you keep ROF -- you change CA, fire the MA, keep ROF, and then your next MA attack is based on its current CA. Any previous CA change doesn't count.