[Galadriel55]

Welcome Idril! I like your nickname!

I can't claim to be the History of ME expert (though some here are), but I'll try to give my two cents on this.

The souls of Men may leave the world upon death, which means that they leave the Halls of Mandos. I don't know where they go, probably to the Void since it's the only place we know about outside Ea. It is said that they will be in Iluvatar's "choir" and will make the second Music after Dagor Dagorath.

I am not sure if the souls of Elves will also leave the world after it is broken and remade. I think that when Finrod died he told Beren something that would suggest that perhaps they would meet again in another world, or something that is just as confusing. I don't have the books with me to quote, but I will do so when I have them.

As for your 1) question, I don't think so. I think Tolkien changed his mind after what you read in Morgoth's Ring (I don't know, I never read it), because there are examples of the opposite. Finrod is one. Some time after his death , he, reincarnated, walked with his father Finarfin in Valinor (which suggests that he was not reborn as someone else). And the more obvious one, Glorfindel. He is the very same one in LOTR as in The Sil. He reincarnated and was sent back to ME.