Since we believe that G-d is Just, that He rewards and punishes, we have to have some reason to say the recipient is accountable for the actions for which he is being judged. It is unfair to punish a rock for falling. Human action has to be different in kind if Divine Justics has meaning.
Rav Eliyahu E Dessler writes (Michtav meiEliyahu vol 1 pp 112) about something he calls the nequdas habechirah, the decision point. To quote R' Aryeh Carmell's translation (Strive for Truth vol vol 1 pp 52):
[Before the advent of modern warfare], when two armies are locked in battle, fighting takes place only at the battlefront. Territory behind the lines of one army is under that army's control and little or no resistance need be expected there. ... In fact, therefore, fighting takes place only at one location, though potentially the line could be drawn anywhere in the territories of the two contending countries.
The situation is very similar with regard to free choice. Everyone has free choice -- at the point where truth meets falsehood. In other words, free choice takes place at that point where the truth as the person sees it confronts the illusion produced in him by the power of falsehood.
But the majority of a person's actions are undertaken without any clash between truth and falsehood taking place. Many of a person's actions may happen to coincide with what is objectively right because he has been brought up that way and it does not occur to him to do otherwise, and many bad and false decisions may be taken simply because the person does not realize that they are bad. In such cases, no valid choice has been made. Free will is exercised and a valid choice is made only on the borderline between the forces of good and the forces of evil within that person.
It must be realized that this "point of free choice" does not remain static in any given individual. With each good choice successfully carried out, the person rises higher in spiritual level; that is, things that were previously in the line of battle are now in the area controlled by the positive inclination, and actions done in that area can be undertaken without struggle and without choice. In this sense we can understand the saying that "one mitzvah leads to another." (Avot 4:2)
And so in the other direction....
I love this model because it's not absolutist, and actually conforms to personal experience. Since it never crossed my conscious mind to just pocket that nice watch I saw in Target today, it's really hard to call this a free-will decision. It's only when the two sides are in enough conflict for me to have to consciously contemplate my options that my will could actually be free.
Rav Dessler doesn't blame someone for those preconscious decisions, he blames them for whatever they did to move the "battlefront" to the point that it could be resolved preconsciously.
(This would also include decisions not made or made wrongly due to lack of information, or due to physical limitations. A person cannot be held accountable for not flapping his wings and flying.)
As for whether Omniscience limits free will... I would argue that G-d does not know today what I will decide tomorrow. Yes, G-d knows everything, the flaw in that proposition is the word "today" -- G-d is "above time", atemporal. Concepts like "today" and "tomorrow" are things He knows about from the "outside". There is no "today" to His knowing. I think this is the Tosafos Yom Tov's point, when he says that G-d's knowledge of the future doesn't impact free will any more than His knowledge of the past.
Or perhaps we just go with the Or Sameiach's non-answer (Hilkhos Teshuvah, essay titled "HaKol Tzafui"). He writes that the answers are like trying to keep two people warm in a jacket that barely fits one. It's simply not large enough. When you pull it over to cover one, you uncover the other. It's not a metaphor for falsity, but incompleteness. An answer that is correct, but incomplete because our minds aren't big enough get it.