To answer your question about the troop numbers, the troops of the Mongol empire that emerged under Genghis Khan did not consist solely of ethnic Mongols but also various different Turkic tribal groups, such as the Uyghurs and Tatars. Part of the fascinating aspects of the history of the empire is that Genghis Khan spent much of his early period battling various clans within the Mongol groups and the Turkic tribes, forging alliances until finally he was acknowledged as the leader of a united federation of all Mongols and Turkic tribes.How were the Mongols so militarily successful? I heard they were able to amass a mounted army of 150,000 men. Did Mongolia even have 150,000 men? Also, they fought European knights wearing cumbersome armour armed only with swords whereas the Mongols fired armoured piercing arrows.
You are correct also that the Mongols fired armoured piercing arrows, but their primarily strength was their use of arrows on horseback, and the resultant speed from which they could conqueror vast ranges of territory.
Another interesting aspect of Genghis Khan, apart from the more ruthless aspects, was his relative religious tolerance: he had decreed religious freedom in lands under his control and supported domestic and international trade. Thus various Muslim, Christian and Buddhist groups had joined him before his foreign conquests.
http://en.wikipedia.org/wiki/Mongol_Empire
Incidentally, a while back I saw a film which I really enjoyed called Mongol, directed by Russian director Sergei Bodrov (or part Mongol ancestry, in fact) which chronicles the early years of the rise of Temujin, who eventually becomes Genghis Khan.
http://www.imdb.com/title/tt0416044/