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The concept of "free will," as defined in a religious sense is the ability to make choices, the opposite of "predestination," which asserts that all decisions an individual makes are "predestined," decided by a higher power, denying that a person has the ability to choose.
In layman's terms, free will refers to what is:
...made or done freely or of one's own accord; voluntary
Free will in Shakespeare's Hamlet can apply to everything that Hamlet does. If one were to assert that Hamlet is predestined to kill Claudius and die, there would be no question of choice on the young Dane's part. However, free will is central to the plot, for it is Hamlet's struggle about doing the right thing (his "indecision") that ultimately causes his death. His free will destroys him as surely as Claudius' poison.
When the Ghost first appears to Hamlet at the end of Act One, Hamlet tells his friends that the Ghost is an "honest" one, but he has his doubts, for if the Ghost is an honest one, he has exposed the truth of Old Hamlet's death, and has given Hamlet good reason to kill Claudius, but this is a problem: it was considered a mortal sin in Shakespeare's time to kill a king, though the Elizabethans also struggled with the moral and ethical question of whether it was ever acceptable to kill a king: what if he were a murderer, such as Claudius, who had himself killed a king—his brother Old Hamlet?
If the Ghost lied about Claudius and Hamlet kills Claudius, Hamlet will forfeit his eternal soul. Why would the question of the Ghost's authenticity ever come up? Elizabethans strongly believed in ghosts and what they were capable of. Ghosts, they believed, were...
...evil spirits that impersonate the deceased.
The ghost's intent (as it was believed) might be to get someone to reveal hidden treasure, or to carry out some purpose that the ghost could not do himself. (A ghost couldn't make a human do anything!)
[T]he audience has a feeling of dread while they try to determine whether the ghost is there for good reason or if it is a damned spirit.
The Ghost tells Hamlet (and he believes) how horrible it is to die without a chance to confess his sins. Hamlet learns of the Ghost's punishment:
Doom'd...for the day confined to fast in fires,
Till the foul crimes done in my days of nature
Are burnt and purged away. (I.v.14-17)
He learns why the Ghost suffers...
Cut off even in the blossoms of my sin,
Unhouseled, disappointed, unaneled,
No reckoning made, but sent to my account
With all my imperfections on my head. (81-84)
He had no last rites, no communion; he died in the fullness of sin.
Until Hamlet sees Claudius' guilt at the end of Act Four, scene two, Hamlet spends his time looking for proof that would condone his murder of the King. His tragic flaw is "indecision," which indicates that he has the ability to choose.
Hamlet has free about committing suicide. He is sure it would release him of the pain of loss and sense of being betrayed, but he fears what lies beyond death, and knows that God has forbidden suicide. He wishes he could disappear or die:
O, that this too too sullied flesh would melt...
Or that the Everlasting had not fix'd
His canon 'gainst self-slaughter! (I.ii.132, 134-35)
This also alludes to the Christian element of free will to live or die.