My Mormonism is a bit rusty, and perhaps outdated. I thought Jesus, God (Eloheim), and Lucifer were separate beings.
This is true. I am unsure if there is a supreme deity in Mormonism (my guess would be Eloheim, the father of Jesus/Lucifier).
The repeated mention, here, of Lucifer, threatens to lead to some rather misleading conclusions. A common criticism directed at us is to accuse of of believing that Jesus and Lucifer are brothers, and that this implies a higher status for Lucifer than we really believe.
To clarify, we believe that Elohim is the father of all of our spirits. In the spiritual sense, this means that all of Mankind are the children of God, and are all brothers and sisters. Jesus is unique in that he is also physically the son of God as well as spiritually. He was the first of God's spiritual children, and was chosen for his unique role in God's plan for all of us.
Lucifer, also, like all of us, is one of God's spiritual children. So, yes, this does make him a brother of Jesus, but not in any different sense than that in which every one of us is a brother or sister of Jesus. In his arrogance, he proposed a plan of his own, in opposition to the plan that God had already established, and sought to claim for himself a position within his plan similar to the role that Jesus was to fulfill in God's plan. He led a rebellion against God, and a third of God's children followed him in his rebellion. This rebellion was defeated, and Lucifer,and all those who took his side, have been cast down, never to progress beyond that stage of existence. All of us who have been allowed to progress to the stage of being born into the mortal lives we now experience, were among those who sided with God, and against Lucifer.
I believe the teachings of Mormonism say that an ascended Mormon is a god, and each rules a planet.
There's really not a lot of clear doctrine on this point. There is a great deal of speculation and extrapolation, most of it, it seems created by those who look to create an argument against Mormonism.
I would say that what is clear is that we are all the children of God, and as such, we all have the potential to become everything that he is; and that a major purpose of his plan for us is to guide as many as possible of us to achieve this potential.
Now whether it is fair to say that those of us who succeed will be
“a god, and each rules a planet.” is hard to say. To me, that seems like an awfully small-minded view. We know that our God has created worlds without number; so if achieving our full potential means that we will eventually become Gods in the same sense as our own God, then I have a difficult time imagining that any of us who achieve that will be satisfied just to “rule” one planet.
In fact, even the use of the word “rule”, here, seems to miss an important point. It seems to imply that our God has created us just so that he can rule over us, have power over us, and somehow stroke his own ego, and that it would be for similar reasons that any of us would do likewise. Alas, my wife and I have no children, and it appears that we never will, but it is clear to me that if we were to have children, it would not be so that we could “rule” over them. It seems clear to me that if I had children, my purpose would be to help these children to grow up to become adults, and to achieve the fullness of their potential. Why should God's purpose for us be any different; and if, somewhere along the way, we become Gods, why should our purpose for our children be any different?