Alma probably knows little about these people because Alma is relatively new to Zarahemlaite society, and has been spending his time developing the different churches. This suggests that the dissentions had begun prior to the time that Alma showed up in Zarahemla.
Alma is unable to make a decision. Why? If he has authority, why doesn't he exercise it?
The answer again lies in both the newness of the institution of the church as well as the potential social problems the situation highlights. Alma brings them to the king because this is a social problem as well as a religious one. The division into two different belief systems would be difficult on the society, and would require a fundamental alteration of the way in which the presumptions about society worked. Alma could not make this decision on his own, and therefore brings it to Mosiah II.