MANI - Why was Polygamy revealed to the LDS church through the Prophet? Was it because of a lack of men while migrating through the USA? Or Is Polygamy needed so that the large # of spirit children can recieve earthly bodies?

JOEL - Both reasons you mentioned are perhaps part of it. Some men were lost through persecution leaving many widows without husbands, but I think the main reason lies in the scriptures and what Joseph Smith said about it.
Plural marriage was one of those principles that was part of the fulness of the gospel in Old Testament times. In the early days of this dispensation as part of the restitution of all things, the Lord also restored the principle of plural marriage. The Book of Mormon gives us an idea of how God felt about it:

"For there shall not any man among you have save it be one wife; and concubines he shall have none; For I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me; thus saith the Lord of Hosts. Wherefore, this people shall keep my commandments, saith the Lord of Hosts, or cursed be the land for their sakes. For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things." (Jacob 2:27-30.)

According to this scripture the best way to raise up a righteous generation of saints("raise up seed unto me") was for God to command His people to practice the principle of plural marriage. This would help get His church to grow quickly in the begining and become firmly established. But they were only allowed to do it if He commanded it, otherwise it would be considered an abomination.
According to Joseph Smith:

"I hold the keys of this power in the last days; for there is never but one on earth at a time on whom the power and its keys are conferred; and I have constantly said no man shall have but one wife at a time, unless the Lord directs otherwise." (Teachings of the Prophet Joseph Smith, p. 324.)

Well, the Lord did direct otherwise and they obeyed His command for as long as the law of the land would allow.