That question is very clearly answered in the Book of Mormon.
Alma 40:
11 Now, concerning the state of the soul between death and the resurrection—Behold, it has been made known unto me by an angel, that the spirits of all men, as soon as they are departed from this mortal body, yea, the spirits of all men, whether they be good or evil, are taken home to that God who gave them life.
12 And then shall it come to pass, that the spirits of those who are righteous are received into a state of happiness, which is called paradise, a state of rest, a state of peace, where they shall rest from all their troubles and from all care, and sorrow.
13 And then shall it come to pass, that the spirits of the wicked, yea, who are evil—for behold, they have no part nor portion of the Spirit of the Lord; for behold, they chose evil works rather than good; therefore the spirit of the devil did enter into them, and take possession of their house—and these shall be cast out into outer darkness; there shall be weeping, and wailing, and gnashing of teeth, and this because of their own iniquity, being led captive by the will of the devil.
14 Now this is the state of the souls of the wicked, yea, in darkness, and a state of awful, fearful looking for the fiery indignation of the wrath of God upon them; thus they remain in this state, as well as the righteous in paradise, until the time of their resurrection.
Not according to LDS theology. Spirits are very much alive and conscious of their einvironment as we are. In fact, acording to LDS doctrine, spirits are very much like us, in perfect human form, and interact and socialize with each other just as we do. For example, when Jesus appeared to the Brother Jared in the Book of Mormon (before His incarnation), He appeared in a perfect human form, so much so that the Brother Jared expected Him to have flesh and blood like us:
Ether 3:
15 And never have I showed myself unto man whom I have created, for never has man believed in me as thou hast. Seest thou that ye are created after mine own image? Yea, even all men were created in the beginning after mine own image.
16 Behold, this body, which ye now behold, is the body of my spirit; and man have I created after the body of my spirit; and even as I appear unto thee to be in the spirit will I appear unto my people in the flesh.
When Jesus appeared to His disciples after His resurrection, at first they were frightened, thinking that they had seen a spirit. But He replied to them: “Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have” (Luke 24:39). So a spirit is in perfect human form; he/she just doesn’t have a physical body like us; but has a spiritual body that in every other respedct looks like us, which enables them to interact with one another and with their (spiritual) environmemt very much the same as we do.
That is what “hell” does in LDS thoelogy. You call it Purgatory, we call it hell. In either case it is a place of punishment or chastisement, until the penalty has been paid and the sinner has been “purged” of his sins.
Yes; and a lot of other things besides!