“5ish: Would that indicate that if the current holder of Nasi/Moshiach is a Litvak or Sephardi, ChabadShlucha and every other Lubavitcher with her beliefs would have to become a Litvak or Sephardi?”
Are you asking me if they should daven Nusach Ashkenaz or eat rice on pesach or are you asking me if they would obligated to follow the directives and hadracha of that person? If the latter, then yes.
Obviously it would need not to contradict other things brought in Chassidus to be a logical conclusion. I.E. it could not be that someone who is opposed to the shitta of Chassidus in general, or Chabad Chassidus in particular, could be the Nasi Hador because that is contraindicated in Chassidus. That being the case, it would not logically make sense for a person to make a decision based on Chassidus to make a decision that is against Chassidus. So there would need to be some level of internal consistency.
All of the above is purely hypothetical because that is not really what most Lubavitchers believe.