JOEL - Many of these details you ask for have not really been made known to us yet as far as I know, but I will offer my opinion based on what is available in scripture and latter-day revelation.

Joseph Smith received revelations explaining that through Jesus Christ, many worlds are created and inhabited (D&C 76:22-24; 93:9-10; Moses 1:33). Everyone who was going to inhabit those worlds, including our earth, were present in the pre-existence along with Lucifer and his 1/3 of the host.
Two thirds of us all agreed to follow Christ's plan of salvation. Therefore all of us who inhabit all the worlds must have the same opportunities to accept or reject the Gospel of Christ.
God is no respector of persons. Therefore, it makes sense that when Satan and his followers were cast out of Heaven they were sent down to all the populated worlds that exist in the entire universe, not just to our earth. There was only one Lucifer for this universe but his invisible kingdom and influence to tempt us encompasses all of God's creations(If you have been to the temple, think about what Satan said to Peter, James and John when they asked him what he was doing there on earth). If this were not the case, those of the other worlds would not have the same opportunity to overcome temptations and prove themselves like we do on our earth.
Our earth is somewhat "special" considering the fact that the reason why Jesus came to this planet is because it was the most wicked of all of His creations(Moses 7:36). He knew that the inhabitants would be wicked enough to crucify Him, so that He could bring forth the atonement and thus continue the plan of salvation for everyone in the universe.

It is a little difficult to understand through our scriptures what is happening to other people on other worlds. Our scriptures are meant for us, living on this planet at this time. Because of this it sometimes seems like they are talking to us as if we are the only ones that exist in the universe. For example the scripture in Revelation states:

"And the great dragon was cast out, that old serpent, called the Devil, and Satan, . was cast out into the earth, and his angels were cast out with him." (Rev. 12:7-9.)

Here it sounds like Satan and his followers are all on this one planet we call "the earth". However, there are probably similar scriptures on the other worlds that say the same thing, even though they are talking about the same one Satan that we know about.
These things are interesting to think about, but are probably not so important for us to completely understand right now. We have enough to worry about with our share of the 1/3 that were cast out and are tempting us now.