I was Mormon for 10 years and got my endowments in the Washington Temple in July of 1986. I'd like to share my understanding of Mormon Doctrine:
Q: Does the Mormon Church believe that God and Mary had physical sex to conceive Jesus?
A: The Church does not claim to know how Jesus was conceived but believes the Bible and Book of Mormon references to Jesus being born of the Virgin Mary.
In fact, they teach that Jesus was conceived just as all children are conceived. Elohim, their name of God, has a physical, although "glorified" body, and we are all his "spirit children" and were born of his many glorified wives whose purpose is to continue to give birth throughout eternity. Jesus was conceived via a physical relationship between the glorified God and the virgin Mary.
Q: Does the Mormon Church believe its followers can become "gods and goddesses" after death?
A: We believe that the apostle Peter's biblical reference to partaking of the divine nature and the apostle Paul's reference to being 'joint heirs with Christ' reflect the intent that children of God should strive to emulate their Heavenly Father in every way. Throughout the eternities, Mormons believe, they will reverence and worship God the Father and Jesus Christ. The goal is not to equal them or to achieve parity with them but to imitate and someday acquire their perfect goodness, love and other divine attributes.
Again, they skirt around the actual answer. The goal of this life, according to Mormon Doctrine, is to become glorified beings, like God and his many wives, and to have your own spirit family and creation. You can never be "equal" to God anymore than you can "equal" to your parents, but you will eventually become exactly like him, with your own Universe to rule. If you are a man, you will have many spirit wives who will give you and endless supply of spirit child to subject to the same sort of tests the Elohim has subjected his children to.
Q: Does the Mormon Church believe that women can only gain access to heaven with a special pass or codewords?
YES. LOL In order to gain access to your heavenly home, you must have gotten your endowment and a secret name. In a ritual that still resembles the Masonic rituals is was stolen from, each member must pass through the "veil" into the temple each time they go. At the veil you must respond correctly with secret gestures. You must also give your secret name. A man ALWAYS precedes his wife though the veil. You are never, ever to reveal your secret name, even to your spouse except at the veil. Therefore a woman will never be able to know her husband's name until she is resurrected and glorified. When I was a member I actually heard women argue with their husbands, trying to get their secret name from them, because they believed that unless they knew his name, they would not be able to find him if he chose not to be found.
Q: Does the Mormon Church believe that women must serve men on both Earth and in heaven?
A: Absolutely not. Mormons believe that women and men are complete equals before God and in relation to the blessings available in the Church.
Then why can a woman not hold the priesthood? Only as a sealed wife of a priesthood holder can a woman be said to hold the priesthood. Additionally, after the resurrection she will take her place, if she is worthy, as one of many spirit wives who serve their god husband and provide him with an endless supply of spirit children to test and torture for their physical bodies. We are expected, like our own spirit mother who never interferes with her husband, to fulfill our responsibilities with joy and obedience.
Q: Does the Mormon Church believe in the existence of another physical planet or planets, where Mormons will "rule" after their death and ascension?
Technically correct. Each glorified family will rule over a Universe that does not yet exist. It will be a creation of that father god's making. It won't have to be anything like ours.
OTOH, Mormons DO believe that there are many worlds in our current Universe that support life put there by Elohim. They each had their "Jesus". The sentient beings on each of these planets is working toward become glorified beings and ruling their own creations.
Q: What specifically does the Mormon Church say about African-Americans and Native Americans?
A: Mormons believe that all mankind are sons and daughters of God and should be loved and respected as such. The blessings of the gospel are available to all.
NOW. Until the 1978 revelation that extended the priesthood to all worthy men, though, dark skinned people were considered unworthy to enter the Temple. Dark skin, according to the Book of Mormon, was a sign of a sinful nature.
Moses 7:8For behold, the Lord shall acurse the land with much heat, and the bbarrenness thereof shall go forth forever; and there was a blackness came upon all the children of Canaan, that they were despised among all people. [Never mind that we now know that humans started out darker skinned and light skin was an adaptation to catastrophic climate change during several previous Ice Ages]
1 Nephi 12:23 And it came to pass that I beheld, after they had dwindled in unbelief they became a dark, and loathsome, and a filthy people, full of idleness and all manner of abominations.
That's enough for now. But I'm very willing to discuss what I learned in ten years if anyone is curious.