Regarding the sex ratio, I think you might be misreading the data: it's counting all free white women in one category, but dividing free white men into over 16s and under 16s. So it's not that there are twice as many women as men, but that the men are divided into two categories.

As for there being more under 16s than over 16s: during the colonial period and early republic, almost all of the population growth (which was very high) was through natural increase, and so it would actually be quite common for there to be such a large proportion of children in the population. If you look at a population pyramid (which sorts the population by proportions in each age cohort) for a country with a high population growth rate (it's the "expansive" type of the model) it tends to have a very wide base, ie much or most of the population is very young.