In Macbeth Act I, Lady Macbeth says:
Hie thee hither,
That I may pour my spirits in thine ear;
And chastise with the valour of my tongue
All that impedes thee from the golden round,
Which fate and metaphysical aid doth seem
To have thee crown'd withal.
Translation: "All that keeps you from the crown, the same crown that luck and supernatural forces seem to want you to have."
In Act III, Macbeth says:
Translation: "Rather than see that happen, come, Fate, into the arena, And fight for me to the death!"
He shall spurn fate, scorn death, and bear(30)
His hopes ’bove wisdom, grace, and fear.
And you all know security
Is mortals’ chiefest enemy.
So, Lady Macbeth tries to help determine Macbeth's fate. Macbeth tries to be an agent of Fate by killing Banquo and Fleance. And the witches say that fate is anything that is dangerous or makes man vulnerable: "security is the worst enemy in humans." So, fate is anything that Macbeth takes for granted.
In the end, fate is luck, supernatural forces, and a false sense of security, a kind of petty revenge. It's so many different things that it's really nothing at all. Therefore, it cannot be concluded that anyone is predestined or manipulated by fate. But, I believe everyone is manipulated by language. A word is more powerful than any spell.
Concerning Shakespeare's Macbeth, the answer depends largely on the beliefs you bring to the play.
With a modern mindset, which you probably possess, you probably, following a thorough reading and study of the drama, would insist that Macbeth has free will and makes choices, then suffers the consequences.
For an Elizabethan, or someone who believes in predestination, however, plenty of evidence exists in the play that could convince such a person that predestination, or fate, as you call it, is at play.
For instance, if the witches know the future, do they just know it or do they cause it? Is there a line between knowing the future and causing it? Even if one finds rational explanations for the predictions concerning Macbeth (he'll be Cawdor, king, Birnam Wood will move, a man born of a body instead of a woman will kill him), one is still left with the prediction that Banquo's heirs will be kings. How do the witches know that? And, again, if they know it, does a supernatural force cause it?
And free will and predestination were contemporary issues in Elizabethan England, brought into focus by the Protestant Reformation.
In short, Shakespeare is often ambiguous, and this issue, as it is presented in Macbeth, is no exception. You can make a case both ways. My modern mind tells me that the witches are manipulative and Macbeth obsessively ambitious, and he makes choices to get what he wants. But I can argue the opposite, as well.