hmmm... doesnt seem like youre having a problem with BC itself, so ill move this to BC General...
as far as BCMI and BCMP - you should get rid of those programs, really... they are old and outdated and have been known to cause problems... you should look into using
Bridge Commander Universal Tool (aka BCUT) instead... that program does everything those others did, and a whole lot more...
as far as BC Supermod, that mod really wasnt designed to work with any other mod at all... it is generally meant for its own BC install, with nothing else added onto it... most people have 2 BC installs when they want BC Supermod for SP (one for BCSupermod only, and another for modding)...
however, thats not causing a problem either... BC Supermod was designed to make SP much much harder; there have been a handful of people that felt the HPs were way too strong and barely possible to play... you can adjust any of the ships HPs (using BCUT's hardpoint tweaker) to make the ships perform more to your liking (as far as in battle)... if youre not sure about that, you could make a thread specifically for that subject in BC Modding forum...
personally, ive never tried BC Supermod so i really cant suggest anything to go about getting through the missions or about the ships weaponry... perhaps there are others out there who have played BC Supermod and can post input about how SP performs with it, and how ships perform?