The following is from the Barsaive Campaign Set, 1st ed.
In this boxed set, The Barsaive Gamemaster Book had the following (pp. 6-8):
"This section provides estimates for botk the general and area-specific racial composition of Barsaive. These numbers do not describe the total population, which remains uncounted since the Scourge. This section shows Barsaive's total population distribution, the distribution of each racial population in the province's three major geographic areas, and the breakdown of population in each geographic area. ..."
It gives figures for estimated racial composition (% of total population): Dwarf 32, Ork 19, Human 16, Troll 13, Elf 10, T'skrang 8, Obsidiman 1, Windling 1.
An Explorer's Guide to Barsaive in this same boxed set includes the following (p. 30):
"Though each of the Name-giver races contributes to Barsavian culture, the influence of each race on a given area differs according to its numbers in that area. The province of Barsaive can be divided into three broad regions: the Kingdom of Throal, including its recently constructed cities; the lowlands, which include most of the province's jungles, the Serpent River, and so on; and the highlands, which include all the mountains and plateaus of the province. All Barsavian cities outside of Throal lie in the lowlands; many smaller villages and towns lie in the highlands.
"Each of the three regions contains the following percentage of Barsaive's people: Throal, 33 percent; lowlands, 50 percent; highlands, 17 percent. Note that one-third of the province's population lives in the kountain kingdom of Throal. Half the population lives in the lowlands, with half of this number residing in the cities. This means that the great lowland jungles of Barsaive support slightly more than a fourth of the province's population. Though the Scourge ended more than 80 years ago and we can now travel the land freely, most people, from habit or wisdom, prefer to cluster together."
This set does not give the population numbers. A 3rd ed. source gives the number of Throal denizens at 190.000, which means a Barsaive population of 570.000. (It may be that the Throal: The Dwarf Kingdom 1st ed. sourcebook gave the number already but I don't have it handy to check.)
That much for total population.
As for the adept population percentage and distribution, I do not know of any reference. I can only guess, and my guess is that they had left this out on purpose so that the GM have a way to define it as it suits his style and campaign ideas. I feel happy with having many NPC adepts in the campaign (around 5-10 percent, if I have to put a number to it. This way, heroes and heroism are a close and tangible presence in Barsaive, and it makes low-circle characters one of us, the people, and its only the higher circles tkat are the stuff of legend. Also, with many adepts, you can freely throw adepts enemies at the party, without background discrepancies.