I haven't read the books (yet! calm down!) but my friend says that elves have the choice to become mortal or remain immortal. Why would Arwen choose mortality? I know she loves Aragorn, but is there another reason? For that reason, why would any elf give up immortality? Why would elves fight at the risk of being killed?

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"Diplomacy is the art of saying 'nice doggie' until you can find a rock." -Will Rogers

If I remember well, elves have to choose between sailing to Valinor and staying in Middle-Earth until the end of the world.
Most Elves will actually return to Valinor, because they know their time is over and they are bored of Middle-Earth.

Elrond, and his children (Arwen, Elladan and Elrohir) are Half-elves : they come from an union of an Elf and a Edain (human).
They have to choose between sailing to Valinor and become immortal (= they choose the elven path), or stay in Middle-Earth and die ( = they choose the human path).

Why does Arwen stay in Middle-Earth? I suppose because she loves Aragorn and she doesn't want to live forever but without him?

Remember that Elladan and Elrohir (Arwen's brothers) decided to stay in Middle-Earth, to fight amongst men.

Only Elrond and his children, as Half Elven, could choose mortality. Elrond's brother Elros chose mortality and became the first King of Numenor, so he was Aragorns ancestor. When you die in Middle-earth, you go to the Halls of Mandos, which is purgatory. Once your time is up, you go to one of several places:dwarves hang out with Aule, Elves go to Valinor and Humans leave Middle-earth entirely to live with Illuvitar (or Morgoth if you worshipped him). So choosing to be mortal is a much bigger choice than you would think, it means that you are no longer bound to Middle-Earth, which would be a huge advantage if Morgoth ever claimed full victory.

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In tolkein's mythos, no one knows what happens to men after death. As their souls were not bound to arda, as were the valar, elves, dwarves, etc., once they left the halls of mandos, no one knows what happens to them.

Well, it is known that they leave Arda, which leaves 3 options. 1. They stop existing altogether. 2. They get consumed by Morgoth. 3. They join Illuvitar. Since death was called the "Gift of Man", and since Tolkien was Catholic, it would have to be number 3, with some of 2 mixed in for the most wicked men.

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"Leave Sauron to me."
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You assume too much. Religious views aside, Tolkien never asserted men are absorbed by morgoth. If they were, it would cancel illuvitar's gift. Men are not bound to Arda. Nor did he assert that they join Eru. The only thing Tolkien said is that no one knows what happens to the souls of men, not even the valar.

And you completely ignore the personal views of the author. Tolkien didn't like purposefully including allegory in his writing like CS Lewis did, but he also said (to Lewis) that any beliefs he had would show themselves in his writing, because he would unconsciously be influenced by his own beliefs. I agree that men being absorbed by Morgoth would kind of "cancel" the gift, but at the same time that was Morgoth's entire goal. If Morgoth could corrupt elves into orcs (basically corrupting the Gift of the Firstborn), I don't see any problem with him corrupting the Gift of Men, which Sauron pretty much did for the Numenorians.

While it is never confirmed, we can make educated guesses as to what happens to men. What we really don't know is what happens to Hobbits and Orcs.

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"Leave Sauron to me."
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I don't disagree that elements of Christianity are present in Tolkien's mythos, the allegorical representation of Eru as God and Morgoth as Lucifer are glaringly obvious, as is the death and resurrection of Gandalf. However, Tolkien makes no indication that the final destiny of men is to live in the presence of Eru or Morgoth. He is however, very specific regarding the fact that men are not tied to the destiny of Arda and are released from it upon death. That is all we know. It seems presumptuous to conjecture one's opinion as fact when the OP has asked for the "facts" regarding Tolkien's mythos. Additionally, Tolkien drew from Norse mythology as much as Christianity to write his epic, with that in mind, attempting to match 1:1 the elements of Tolkien's mythos to Catholicism (Halls of Mandos:Purgatory) completely ignores the fact that many other epics he read influenced his writing.

I'm not saying that there is no parallel between the Halls and Purgatory, or the LOTR afterlife and the Christian afterlife, only that the symbolism (intentional or accident) go beyond Catholicism.

In regards to the hobbit afterlife, according to the one ring wiki (such a scientific reference, right;) ) Hobbits are a subset of men thus are entitled to gift of men as well.

I can't speak for orcs. On the one hand, they were created from elves who were corrupted, which would lead me to conjecture that they inherit the gift of the first born. However, we know that isn't true because there is no mention of the orcs wandering around in the halls of Mandos. On the other hand, as they have fallen from grace (a common and powerful theme in LOTR) they receive no gift and cease to exist upon death. Having said that, I will add, this is only my opinion formulated on my understanding of the Tolkien mythos and I have nothing to support that claim.

As a final note, Draugluin, I am engaging in a friendly debate and do not wish to offend, regardless of our interpretation of the LOTR afterlife, I will not flame or call you names . If my language comes across as strong, it is unintentional (even if that means we have to agree to disagree).

Well, he didn't ask for facts, but I guess I did present my opinions as facts. However, there is nothing outside of Arda save for Eru, Morgoth and the Void, so it really wouldn't be a blessing to die if you just hung out in the void. Putting 2 and 2 together and getting 4 isn't the craziest thing in the world, even you don't necessarily agree that it is 2 and 2. As a Christian (so I recognize the Biblical similarities pretty easily) and as someone who has looked into Tolkien's own beliefs, I feel pretty confident that my conclusions are pretty close to being correct. Maybe if he had actually finished the Silmarillion, it would be more obvious. After all, it was his son who collected and published his notes.

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"Leave Sauron to me."
If you're in the Raleigh, NC area, let me know.