JOEL - Mohamet(Muhammad) as a proper name usually refers to the Arab prophet who founded Islam (570-632 AD). But as a noun it can also refer to any prophet who speaks by divine inspiration; someone who is an interpreter of the will of God. This deffinition fits the mission of Joseph Smith, who also considered himself a prophet of God. He may have used the comparison to simply help others (perhaps those of the Islam faith) to understand the importance of his calling.
The Islam faith had no influence on the decission to practice polygamy. This was a revelation and commandment directly from God to Joseph Smith.
Your reference to Egyptian and Coptic connections are only relevant in the few general similarities that are found in the many sacred ceremonies that existed in the ancient world compared to the temple rituals found in the Mormon church today. Modified over centuries, similar rituals existed in some form among ancient Egyptians, Coptic Christians, Israelites, and Masons, and in the Catholic and Protestant faiths. Common elements include the wearing of special clothing, ritualistic speech, the dramatization of archetypal themes, instruction, and the use of symbolic gestures. Though these ceremonies vary greatly, significant common points raise the possibility of a common remote source. However, the ceremonial rites performed in the Mormon temples today were received by revelation from God to the Prophet Joseph Smith.