The nature of Prophecy in Middle-earth

Various times in LotR, characters make or receive prophecies. Boromir and Faramir had the mysterious dream. Who sent it? (It's possible this was explained but I just forgot ) Long before the War of the Ring, someone foretold that the Witch-king would not be slain by a man, that the King could be told by his "healing hands," and various other things that I can't recall at this moment. Everyone seemed to take these prophecies for granted as absolute truths; the Witch-king even gloated that he couldn't be killed by a man. Does that mean that if a man happened into the circumstance that Merry and Eowyn did, he wouldn't succeed because of some odd force relating to prophecy?

Then some characters make on-the-spot predictions. Theoden predicts that he won't return from the battle. Saruman predicts that Frodo won't have a long life. Then right before the voyage to Aman, Frodo tells Sam the name of his future children. What gives him this power? If Frodo hadn't said anything, would Sam have named the children that anyway? What if he decided NOT to name his children that because of what Frodo did? (Well, we know from the family trees that they did get those names.) The interesting thing is, did Rosie "think" of those names? If Sam did, it's not really a prediction, but rather a recommendation by Frodo.

So, do the Valar responsible for all this? (And did I make a dumb topic again? )