Re: the number of factions, I guess the upper limit depends on what you see their role in the tabletop game as being.
If they are there as flavor/window dressing just to provide context to all the robot-stomping going on (e.g. if, as mentioned in the thread, you want to play mercenaries who fight for anyone), then I think you'd be guided by having a clear flavor for each. If faction B is just faction A with a slightly different paint job, then it probably isn't adding anything to your setting. In addition, particularly for a game like BTech that wants to expand its player base, the upper limit should perhaps be set by how easy it is for a beginner to understand--e.g. if you can't describe it in 2/3 keywords, it's probably too complicated.
If on the other hand factions are intended to have an impact on gameplay, so that the game itself plays differently depending on which faction you choose, then the range of distinctive play styles should perhaps limit the number. e.g. Faction A is good at melee, Faction B has a small number of powerful units, Faction C has a swarm of lighter ones, D is good at sneaking/hiding and ambushing, etc. If there's no clear differentiation in the way its units function in combat, cut the faction.