OK, to address these in reverse order.
1) The pendant was an invention of the movie, and while it was a nice symbol of Arwen giving Aragorn her heart, there's no suggestion either there or in Tolkien that immortality was or ever could be contained in an object. It's a token - think of a knight's lady giving him her kerchief before he rides off to the wars.
2) Legolas is an Elf. All Elves are immortal (even those rare exceptions like Luthien Tinuviel and Arwen who give it up later on are still born immortal). Therefore Legolas is immortal.
3) Arwen's mother is spoken of in the appendices and I *think* in Unfinished Tales (sorry, I know I've read about her somewhere, just can't remember the name of the source). She was waylaid by Orcs while traveling between Rivendell and Lothlorien and was "tormented" - details are not specified. She survived, but was so badly hurt that she found it necessary to take ship to the Undying Lands a year later to be fully healed, thereby leaving Elrond with the twins and Arwen to take care of. The impression left is that if she had not been attacked, Celebrian would not have left so early. But she is alive.
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Father, dear Father, if you see fit, We'll send my love to college for one year yet
Tie blue ribbons all about his head, To let the ladies know that he's married.
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