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Answer: Eldarion was mortal because his father, Aragorn, was a mortal and his mother, Arwen, chose mortality. He was not given the choice between mortality and immortality because he was not considered half-Elven. Both his parents were mortal.
Question: What were the names of Aragorn's children?
Answer: Aragorn had one son, named Eldarion who was his heir. He also had "daughters" who are vaguely mentioned in Appendix A. (Then [Arwen] said farewell to Eldarion, and to her daughters,...")
Question: What is Numenor?
Answer: Numenor was an island in the far west given to the mortals (more specifically the Edain) because they chose to help the Valar during the War of Wrath against Morgoth. The island was shaped also like a star. Its first king was Elros, Elrond's brother, who chose mortality over immortality. The island was drowned by Iluvatar (God) when the Numenoreans tried to attack Valinor, being decieved by Sauron into thinking that they would obtain immortality if they stepped on its shores. A few of those still loyal to the Valar and who opposed this attack escaped and established the realms of Gondor and Arnor in Middle-earth. The decendants of Numenorean kings were the Dunedain, this included Aragorn.
Question: Where is Valinor and why do people go there?
Answer:
Valinor is the island in the furthest West that was separated from the world at the end of the Second Age when the world was made round during the destruction of Numenor. It is considered paradise because of the Powers (or Valar) that live there. The Elves sail there at the end of the Third Age because the world is being usurped by Men and the Elves no longer have a part in its history, so they sail to Valinor. If they do not, they will fade like shadows and diminish so that mortals cannot see them.
Question: How come all the Elves have bows and arrows?
Answer:
All the Elves do not have bows and arrows. Feanor wielded a sword, so did Beleg, Fingolfin, and many others. Gil-Galad wielded a spear. But Elves were excellent archers because of their superior eyesight. For example, Legolas saw the Riders of Rohan from afar when Aragorn and Gimli could not.
Question: What powers do the Elves have?
Answer: The Elves do not have "powers" or "magic." In the Mirror of Galadriel, Galadriel says, "This is what your folk would call magic, I believe; though I do not understand clearly what they mean; and they seem to use the same word for the deceits of the Enemy. " In the Preface of the Silmarillion, it clearly states that magic and power is strictly the works of enemies like Sauron or Morgoth. The Elven "powers" therefore, are rather a form of art. It also states that the closest that the Elves have ever gotten to magic were the Rings of Power. The art of the Elves are known for thier agelessness and healing properties. Thier works never seem to whither or grow weary over time. For example, Frodo felt that he was in a "timeless land that did not fade or change or fall into forgetfulness." The art of the Elves made it appear so.
Question: Is Aragorn half Elven and if he is, was his mother or father an Elf?
Answer: Aragorn is not half Elven although he does have Elvish ancestors. The first king of Numenor was Elros, brother of Elrond, is the son of Elves with mortal blood, and so he was given the opportunity to choose between mortality and immortality. Although he chose mortality and became the first king of the Numenoreans, he still had Elvish blood. Aragorn is related to Elros, as a decendant of the kings of Numenor. Because he is related, Elrond fostered the cheiftains of the Dunedain in Rivendell out of memory of his brother.
Question: Are the Istari immortal?
Answer: Yes, the Istari are immortal. They were originally Maiar, spirits made by Iluvatar before the world, like the Valar but lesser. To learn more about the Istari, visit this link: Wizards