What is it?
Do we really have free will?
How does God's nature and character relate to free will?
First, you have to define what is meant by free will. Is it freedom to choose anything I want? If so, then desire is a major factor, as well as the possibility of what is chosen. For instance I may want to walk on the moon without a spacesuit and not die, but it is impossible, therefore I cannot really choose to do so. Therefore, free will has limitations, but those limitations do not diminish it in and of themselves.
So, we must conclude that only what is possible is within the realm of free will. But, what is possible for an individual is limited by other factors beyond their control, like circumstances, availability, opportunity, and the like. Therefore we must conclude that free will is limited to what is available, what circumstances will allow, and what opportunities are present and available. This also is not a limitation of free will, it is just dealing with reality.
What limits the will of man is his own desires, which cause him to choose according to his strongest desire with every choice he makes. Some would argue for "autonomous free will", but such a concept collapses when one realizes that all men are affected by outside influence, either from Satan, or from God. Autonomous means to be free from outside influence or control.
God's influence in those whom He saves is to monergistically change their desires, by way of the new birth (regeneration) to desire righteousness and holiness, where before they desired sin and wickedness. Those who are unregenerate are influenced by Satan, who tempts and draws them into sin, and more sin, things which unregenerate men naturally desire.
Men are not autonomous, because they are influenced and controlled by their passions, and sinful desires, if they are unsaved, or they are influenced and guided by God in righteousness and holiness if they are saved. They are free within the bounds of those definitions and parameters to make choices, but those choices are not free in the sense that they are entirely self-generated.
As has been pointed out, God knows all of our choices before we make them, and has incorporated those Foreknown choices into his Purpose and Plan, and affects what choices are available to us at every point of choice. We freely choose to do say, and act exactly as He has Foreseen and Foreknown that we will choose and do. He leaves nothing to chance, but "all is open and naked before Him with Whom we have to do."