Hamlet Act I Scene 3-5

Act I scenes 3-5 addresses many issues and topics that are still prevalent and relatable today, regarding romantic relationships, virginity, youth, sibling and father relationships, and issues regarding faith and religion. Act 1 Scene 3 follows Laertes and his sister Ophelia, the children of Polonius, before Laertes leaves for France. Laertes gives advice to Ophelia regarding her romantic relationship to Hamlet. Laertes is around the same age as Hamlet, so he is able to understand the intentions of a young man - which he warns Ophelia are usually immature and lustful. He says, "Then weigh what loss your honour may sustain / If with too credent ear you list his songs, / Or lose your heart, or your chaste treasure open / To his unmastered importunity (1.3.29-31). Although Ophelia believes that Hamlet truly loves her, Laertes knows better and warns her not to give away her innocence thoughtlessly. I found this advice interesting because it addresses issues that girls today deal with. A timeless struggle is the immaturity of young men and how they care about sex above all else, leading to girls getting their hearts broken. Laertes' advice therefore can still be useful regarding relationships.
Act 3 also brings up another important theme - father-son vs. father-daughter relationships. Polonius has just finished giving advice to Laertes, regarding his move to France, including to not speak without thinking, avoid judgement, be careful with whom he chooses to be friends with, and take caution regarding how much he spends and what he wears, as "the apparel oft proclaims the man" (1.3.72). In comparison, the advice Polonius gives to Ophelia solely revolves around her relationship with Hamlet. Polonius tells Ophelia, "I do know / When the blood burns, how prodigal the soul / Lends the tongue vows... Be something scanter of your maiden presence" (1.3.114-117, 121). Like Laertes, Polonius urges Ophelia not to believe Hamlet and be careful with her virginity because his intentions are most likely more lustful and political than anything. In comparison to the advice given to Laertes, Polonius' advice to Ophelia is more condescending and is only about her relationship. This is symbolic of the difference between the way men and women were seen at the time. Laertes has so much potential and so many options for his future regarding his education, friendships, and money, whereas Ophelia's only importance is her virtue and her only future revolves around who she will marry.
In Act 5, Hamlet finally speaks to the ghost of his father. We learn that King Hamlet was poisoned by Claudius, and King Hamlet had not confessed his sins at the time he was murdered, so he now sits in the torture of purgatory. He asks his son to get revenge on Claudius, and we see the loyalty of Hamlet. He is so willing to obey his father and is determined to take revenge. He makes a plan to act crazy, and commands Horatio and Marcellus to swear not to tell anyone about seeing the ghost of King Hamlet, nor about how he will pretend to be crazy.
I am confused if Hamlet is really going crazy or why he is going to pretend to be? Also, are Horatio and Marcellus avoiding swearing not to tell?