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As Eru is omniscient, one might think that there is no free will. Plus, as the Music was sung before Arda was made, it would also seem that everything has been plotted/doomed/fated.

Not sure that I agree.

My other favorite author, Frank Herbert (of the Dune series) explored the free will/fate/god question. He posited that a god may want to allow true 100% free will just to relieve the boredom. It would be like watching the same movie night after night - wouldn't it be cool if one time, while watching ROTK EE, Gandalf's staff doesn't break? But I digress.

Anyway, could not Eru have set up the 'rules of the game' (stuff falls down not up, time moves forward, etc), created the original set of actors (valar, maia, elves, men, etc), established his own plan (introduction of the elves at X year, men to show up later, etc) and then sit back and watch how it all plays out?

The evidence gleaned from the actions of Melkor (rebellion), Aule (dwarves), men, etc, would point to free will. Now, it's still Eru's game, and at any time he can change the rules, dabble, or destroy the whole show as he desires. The actors therein can do whatever they feel is the correct choice, but Eru, being the smart god that he is, knows that with some probability that certain outcomes are assured.

Think about it. In the beginning we have only one vala go sour. What if more went against Eru? Would Arda have become so lopsidedly bad that Eru's game would have been spoiled and so he would have had to start over.

Hmmm. What evidence do we have that this time is the first and only time that Eru played the game? What if he tried some other combinations, gathered data, experimented more then finally got a game set up that would provide maximum entertainment/glory while also maximizing the free will of the actors therein?

Gods, being without limits by definition, can do these kind of things...