Everyone, except certain unfortunate individuals, is predominantly one sex or the other. Does this persist through incarnations, or do we alternate sexes?

The predominance of one sex or the other will persist through the incarnations. We do not come back alternating one sex with the other, as some teachings affirm, although everyone must have some experience of life in the complementary sex, and there is an average ratio for this. When, perhaps for kharmic reasons, an entity predominantly one sex must reincarnate in a physical body of the complementary one, if the change is more than can be accepted there is a feeling of incompatibility with the physical body, and this is one of the causes of homosexuality.