In Hamlet, how does Laertes develop as a character through the course of the play?Please provide some details or examples from the play.
You asked quite a few questions about Laertes, and, since you may only ask one question per submission, I have chosen what I believe is the most signficant of the questions you asked.
Laertes spends a good deal of this play offstage and in France. We meet him briefly in Act One, scenes ii and iii. He speaks in a very courtly manner in scene ii, when he asks Claudius' permission to return to France, and, already, there is a clear comparision drawn between him and Hamlet, who is belligerent and refuses to behave in a way that becomes the son of a king in this very public court scene.
In Act I, scene iii, Laertes is saying his farewells to his sister and father. To Ophelia, he has cautionary words about Hamlet. He tells her that she should be careful with her virginity around Hamlet, as he is a Prince and might be playing around with her, but with no intention of marrying her. With his father, he endures Polonius' long speech about the ways he should conduct himself in the world, the sort of carefully planned, almost two-faced presentation of himself he should make. This speech seems to make almost no impression on Laertes. As soon as Polonius is done, he turns right back to Ophelia, reiterating what he has said about Hamlet.
In Act II, scene i, though Laertes does not appear, we learn much about how straight-laced and honorable Laertes is, because Polonius is sending Reynaldo to France to sully up his son's reputation a bit, so that he might seem more of a man of the world to his fellows.
Laertes re-appears in Act IV, scene v. He has returned to Denmark for revenge. He enters with every intention of murdering Claudius right then and there, assuming that the king was responsible for his father's death. Again, this casts him in direct contrast to Hamlet, who has hemmed and hawed throughout the course of the first three acts of the play unable to avenge his own father's death. Once Laertes is calmed down, he is apprised of Hamlet's guilt concerning Polonius' death. Laertes immediately enters into a scheme with Claudius to kill Hamlet. For Laertes, there is no hesitation towards revenge, and the witnessing of Ophelia's madness and her death only add fuel to his fire.
When Hamlet appears at Ophelia's grave, Laertes must be restrained to prevent him from killing Hamlet then and there. Again, his decisive and knee-jerk impulse towards revenge contrasts with Hamlet's ponderous, overly-analytical hesitation towards his own revenge.
At the end of the play, Laertes realizes the role of villain that Claudius has played all along, and makes his peace with Hamlet as both are about to die. Withdrawing his hatred of his father's murderer and going so far as to forgive him the act is a forgiveness that Hamlet is not willing to grant Claudius.
Since Laertes spends so much of the play offstage, I'm not sure how much development the audience can see from him, but he does serve the very important function of being a foil to Hamlet. His actions are the exact opposite of Hamlet's response to the very similar circumstances in which they find themselves.
For more about Laertes and how he contrasts Hamlet, please follow the links below.