I honestly am unsure of how
Men tie in with the Fate of
Arda, but I believe that Men's decisions led others down a certain path, but that path was already made, just not the only one to be taken. I know I'm being confusing here, so let me try and clarify what I mean:
The Fate of Arda is completely pre-determined, but the choices of Men change that predetermined path. It's like Fate was traveling within a maze that starts from one point, branches out into practically infinite paths, but all the paths ultimately converge in the end upon two possible conclusions, and every time a Man made a choice that effected others, Fate comes to a fork in the path, and that decision decides which way Fate will go. But that Path is still already made, all that is unknown is in what way Fate will arive at the end, but the end will be
the one of two pre-determined
events. If Men make enough bad decisions, the path Fate takes will lead it to the bad of the two ends, and visa-versa. All the things
Elves and others do in reaction to what Men do are pre-determined; If
Beren chose to go after
Lúthien and Met her, then she was destined to marry him and become Mortal, bit if Beren didn't, then she would live out a different, but still pre-determined, fate.
If that's confusing, I understand why. But whatever. Of course there is another theory that, to me, seems more realistic:
The Fate of Arda was pre-determined, but the Fate of Men was not, and when Men made decisions that directly affected the Fate of Arda, Arda's Fate changed in whatever ways they were influenced in. For example, I do not believe that even
Ilúvatar knew that
Sauron would corrupt then Númenoreans and convince them to attack
Aman. He may have known that Sauron would try to do so, but whatever Men decided to do was entirely up to Men, and neither he nor anyone knew what they would choose when given certain circumstances.
Eru was then furious with the Númenoreans for having chosen so poorly and therefore cast their land beneath the Sundering Seas. The Fate of Arda was unknown by all because the choices of Men allowed for too great a variable to allow prediction of prior knowledge. If
Isildur had cast
the Ring into Orodruin, Sauron would have been ended forever and all of
Middle-Earth could regain at least some peace. But if he didn't, Sauron would live on with enough strength to wield great
evil still. The choice was up to Isildur and Isildur alone, and what he chose nearly brought an end to good in Middle-Earth. It was then the choices of others that would decide the outcome of everything, for though Isildur repented when he was attacked by
Orcs two years after recieving the Ring and attempted to escape with the Ring to
Rivendell in order to have it brought back to
Mordor and destroyed, he was slain in the Gladden
Fields, upon the shores of
Anduin, and it was no longer his choices that would lead the fate of the World. But my point here is that no one, not even Ilúvatar, knew what the outcome of the World would be. It was up to the
Ainur to attempt and accomplish what Eru and they had created. The choices of Men would influence this, possibly influence others to do things that they would not have otherwise done (such as Sauron corrupting
Númenor, which I don't think even Eru knew would happen, because it only happend as a result of something Men did). But if the Ainur would fail or succeed, none save maybe Eru alone knew, and even he did not know in what way the world would unfold that would result in the accomplishment of his will. Again I say this is just a theory I have.
Now, as for Free Will, I suppose no one had free will but Men. It was fated that Lúthien would love Beren and would thus want to marry him, so essentially you could say that everyone did what they did because of their hearts, and their hearts being pre-determined therefore made their choices also predetermined. As for Men, their decisions too were all based upon their hearts, but since the Hearts of Men were what was unknown and different from everything else, their choices were also unknown and impossible to predict.
But these are just my thoughts, and I'm not confident that they are necessarily correct.