My personal feeling is that Eru gave free will to all his "children," both the Ainur and the Eruhini. The Valar have certainly done things Eru would have rather they didn't. Why would He have chastized them for bringing the Elves to Aman and not trusting Him to protect them while they dealt more expediently with Melkor if they had not chosen a path that went contrary to His will? In fact, if all beings but Men are bound to the Fate of the Music, then how is it possible for any of them to make mistakes? All pain and suffering and horror, no matter how awful it may be, must then have been a part of the Plan, and nothing that is done can circumvent or alter the Destiny that was laid down in the Music.
For myself, I can't buy that. It seems very apparent to me that all of Eru's thinking creations have the options of free will. The one great difference between them is Death. Men know they are going to die, and pass beyond the circles of the world. The Elves and the Ainur of Ea do not. While the Ainur can reasonably presume that they will return to the Timeless Halls and rejoin the rest of their brethren after the end of Ea, the Elves do not know what will become of them. Men, on the other hand, have in their mortality a certainty of what will become of them. If they believe that Death is a gift, and that through it they will pass into another life outside the mortal world, they know that there is more for them beyond it, and that whatever they might have suffered in their life before death, there is hope for a second chance after. If they don't believe it, they at least know that their pain and suffering will end with death. Not so for the immortal. The Elves have either the "imprisonment" of Mandos or a return to the same old life in the same old world to look forward to. The Ainur do not die, and though they may become diminished and impotent, they too are trapped. Only through Death is there a way out of this seemingly vicious circle.
And mortality, with its limitations, also gives an impetus to achieve. If you don't do it now, when will you? Can you wait forever to get around to doing or learning or building, or even loving? The Elves and the Ainur do not feel the press of time in the same way; they may have ambitions, but there is seldom the same sense of immediacy to them as there are with Men -- they CAN take their time, because they've got a lot of it ahead of them. And in this, one can see why it is also said that toward the End, even the Valar would become weary of the world. By then, it will likely have become a cage from which they cannot escape because of their bargain with Eru, made when they entered Ea. They have lost the freedom to go beyond it, and the Elves were designed to remain within it. But not so with Men. To beings stuck in an inescapable cage, being set free through Death would indeed come to envied as a Gift.
I have other thoughts about how this reflects on the events surrounding Gandalf's death and return to life (especially as Tolkien discusses it in Letter 156), but that's another kettle of fish.
