1) We believe that Satan does not have and will never have a physical body. Isa. 14:12:
How art thou fallen from heaven, O Lucifer, son of the morning! how
art thou cut down to the ground, which didst weaken the nations!
And then, D&C 76:25-27:
And this we saw also, and bear record, that an angel of God who was in
authority in the presence of God, who rebelled against the Only
Begotten Son whom the Father loved and who was in the bosom of the
Father, was thrust down from the presence of God and the Son, and was
called Perdition, for the heavens wept over him—he was Lucifer, a son
of the morning. And we beheld, and lo, he is fallen! is fallen, even
a son of the morning!
And finally, D&C 29:36-38:
And it came to pass that Adam, being tempted of the devil—for, behold,
the devil was before Adam, for he rebelled against me, saying, Give me
thine honor, which is my power; and also a third part of the hosts of
heaven turned he away from me because of their agency; and they were
thrust down, and thus came the devil and his angels; and, behold,
there is a place prepared for them from the beginning, which place is
hell.
We discussed hell and Perdition answering your last set of questions.
The LDS Church believes that all people existed spiritually before the Earth was created. During that "premortal existence" a council in heaven was held where our Heavenly Father presented his plan for our progression. (We believe Job 38:4-7 also refers to this council.) Lucifer's rebellion against our Father's plan sparked the War in Heaven referred to in Rev. 12:7-11. Having been cast out, he and his followers (a third of the host of heaven) are denied entrance to the Earth and participation in our Father's plan. Therefore, Lucifer and his followers will not receive bodies.
2) D&C 130:22 teaches the following:
The Father has a body of flesh and bones as tangible as man’s; the Son
also; but the Holy Ghost has not a body of flesh and bones, but is a
personage of Spirit. Were it not so, the Holy Ghost could not dwell in
us.
We know very little about the person we refer to as the Holy Ghost. Being a part of this Plan, as Christ is, Church dogma (vs. doctrine) suggests that He will eventually have the privilege of a mortal body, resurrection, and exaltation. However, even saying that is simply speculative. There is simply no scripture or prophetic commentary that I'm aware of on the matter.
3) Remember that "heaven" is a bit more complicated in the LDS faith. As for where the idea originates, or where the spirits come from, let's start with one verse, D&C 107:20 states:
The power and authority of the lesser, or Aaronic Priesthood, is to
hold the keys of the ministering of angels, and to administer in
outward ordinances, the letter of the gospel, the baptism of
repentance for the remission of sins, agreeable to the covenants and
commandments.
As for where these ministering spirits come from, consider this: before the Earth was created, and speaking only within the realm of this Earth and not on behalf of any other creation of our Heavenly Father (about which we know practically nothing), those of His children destined for this world were all spirits. Lucifer fell with a third the host, leaving 2/3 of the host destined for this world who would actually come to it (having "kept their first estate," Jude 1:6 and Abraham 3:26-28). From the creation of Adam until (perhaps just before) the end of the world there will be spirit children of our Father waiting their turn to recieve mortality on this earth. Excluding Lucifer and his followers (and describing this very simply... there's a lengthy discussion here), people will be receiving resurrection beginning with Jesus and ending with Judgement. Therefore, spirits (call them angles if you like) are available to do the Father's and the Son's bidding until the very end.
