As referenced in 1 Corinthians Chapter 15 (Bible citations KJV)

"40 There are also celestial bodies, and bodies terrestrial: but the glory of the celestial is one, and the glory of the terrestrial is another. 41 There is one glory of the sun, and another glory of the moon, and another glory of the stars: for one star differeth from another star in glory. 42 So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption: 43 It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power:"

Our belief is that everyone on the earth will receive of the glory of God. Some will dwell eternally in Telestial or Terrestrial glory (kingdoms) outside of the presence of God and Jesus Christ, while those who fully accept Christ and receive all that He offers, will live with Them in Celestial glory; Romans 8:17:

"And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together."

So in a sense of "hell" and "fire & brimstone" it is more a state of mind that an eternal location. The Book of Mormon speaks of this in several passages including Mosiah Chapter 3:

"25 And if they be evil they are consigned to an awful view of their own guilt and abominations, which doth cause them to shrink from the presence of the Lord into a state of misery and endless torment, from whence they can no more return; therefore they have drunk damnation to their own souls. 26 Therefore, they have drunk out of the cup of the wrath of God, which justice could no more deny unto them than it could deny that Adam should fall because of his partaking of the forbidden fruit; therefore, mercy could have claim on them no more forever. 27 And their torment is as a lake of fire and brimstone, whose flames are unquenchable, and whose smoke ascendeth up forever and ever. Thus hath the Lord commanded me. Amen."

In essence, torment "is as" a lake of fire and brimstone. For eternity, those who chose the things of the world over Christ and His Atonement and mercy, will have to realize that while they are in a place of His glory, they are not with him and will forever have the realization of what they gave up in eternal relationships.

Outer Darkness is a result of what the scriptures also refer to as the unpardonable sin or denying the Holy Ghost: Matthew 12:

32 "And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come."

(Note: this is also an interesting verse as it relates to the nature of the Trinity and the LDS view that the three members of the Godhead are separate, but that is for another discussion).

In 1 Corinthians 12:3 it states, "… no man can say that Jesus is the Lord, but by the Holy Ghost." If someone has come to know that Christ is the Savior of mankind, that He is the literal Son of God our Heavenly Father, that He is our Creator, that He overcame sin and death, that through Him each of us may also overcome sin and death and live with God forever in His Kingdom and His Glory; this knowledge would have come through a relationship with the Holy Ghost (Holy Spirit). If that knowledge and relationship is then rejected, or in other words, that person chooses to reject the Light given them through Christ, they have chosen to dwell in Outer Darkness (or without any Light from Christ). One is not necessarily cast into Outer Darkness, as much as one would choose to be there by deliberately rejecting the light of Christ.

Hell can be described as a separation from Heavenly Father and Jesus Christ. in this life - those who do not enjoy the knowledge of Christ and the inspiration and comfort the the Holy Spirit - even if they live next door to or work in the cubicles next to someone who does, could be considered to be living in hell (not knowing Christ), after this life, there is an interim space known as the Spirit World where, like here, those who know of Christ will continue to teach those who haven't learned of Him, so that all can have the opportunity to know and be saved through Christ. Then, when all have Learned and chosen, will be the final judgement.

Hell is not a place where we will be tormented or tortured by anyone other then ourselves for our choices and the results (i.e. Why did I smoke all those years when I knew it was bad for me and now I have cancer and won't live to see my children get married or my grandchildren grow up; why was I so selfish and stupid; only on an eternal scale; why didn't I follow Christ and accept of His Grace and now I can't live with Him forever…)

In LDS doctrine, multiple things are referred to as Hell, and none of them can be confirmed as permanent. Here is (hopefully) a comprehensive answer:

Hell

Definitions

Spirit Prison - After death, before the resurrection, being in a state of darkness because of wickedness during life. See D&C 138: 20-22
Outer Darkness - Dwelling place of the devil, his angels, and sons of Perdition - those who denied the Holy Spirit after having received it. See D&C 29:36-38
Spiritual Death - The state of being separated from the presence of God. See Alma 42:9

Is Hell Permanent?

Hell (as Spirit Prison) - NO

D&C 76:84-85
84 These are they who are thrust down to hell.
85 These are they who shall not be redeemed from the devil until the last resurrection, until the Lord, even Christ the Lamb, shall have finished his work.

Hell (as Outer Darkness) - Not Revealed

D&C 76:44-46
44 Wherefore, he saves all except them—they shall go away into everlasting punishment, which is endless punishment, which is eternal punishment, to reign with the devil and his angels in eternity, where their worm dieth not, and the fire is not quenched, which is their torment—
45 And the end thereof, neither the place thereof, nor their torment, no man knows;
46 Neither was it revealed, neither is, neither will be revealed unto man, except to them who are made partakers thereof;

Hell (as spiritual death) - NO

2 Nephi 9:12
12 And this death of which I have spoken, which is the spiritual death, shall deliver up its dead; which spiritual death is hell; wherefore, death and hell must deliver up their dead, and hell must deliver up its captive spirits, and the grave must deliver up its captive bodies, and the bodies and the spirits of men will be restored one to the other; and it is by the power of the resurrection of the Holy One of Israel.

See also: Bible Dictionary - Hell, D&C 19:4-12

To add to Matt's answer, and speaking to question 3,

Is anyone tortured in hell or in the "outer darkness" according to LDS beliefs?

Doctrine & Covenants Section 19 answers this question well. It also speaks about the punishment in hell (the temporary one in Matt's answer) being a punishment that has an end. I would recommend reading verses 1-20. I quote a few verses here to provide an answer.

4 And surely every man must repent or suffer, for I, God, am endless.

...

15 Therefore I command you to repent—repent, lest I smite you by the rod of my mouth, and by my wrath, and by my anger, and your sufferings be sore—how sore you know not, how exquisite you know not, yea, how hard to bear you know not.

16 For behold, I, God, have suffered these things for all, that they might not suffer if they would repent;

17 But if they would not repent they must suffer even as I;

18 Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit—and would that I might not drink the bitter cup, and shrink—

19 Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men.

20 Wherefore, I command you again to repent, lest I humble you with my almighty power; and that you confess your sins, lest you suffer these punishments of which I have spoken, of which in the smallest, yea, even in the least degree you have tasted at the time I withdrew my Spirit.

So, those who do not repent must suffer. Although I don't have a good reference right now to demonstrate this, as a Mormon I have always been taught that this suffering is suffering for one's own sins (suffering the punishment thereof) and that this suffering occurs in hell. Those who commit the unpardonable sin against the Holy Ghost (another question for another time) will go on to outer darkness, where their suffering has no end. Those who do not repent but do not commit the unpardonable sin, I have been taught, have their suffering occur in the temporary hell that Alma describes in Matt's answer, which has an end.