In Act 2, sc. 2, what's Hamlet's state of mind revealed by his soliquy? What do Hamlet's remarks to Polonius tell about Hamlet's thoughts?
In his third soliloquy (act 2, scene 2), Hamlet recriminates himself for his lack of courage, which prevents him from avenging his father's murder.
After watching an actor make a bold, grief-stricken speech over an imaginary loss, Hamlet derides himself as "a rogue and a peasant slave." (2.2.506) He wonders if he is nothing more than a coward because he should have already "...fatted all the region kites/With this slave’s offal." (2.2.540-541) Hamlet concludes that he must be cowardly; otherwise, he would have slain Claudius, the "bloody, bawdy, villain" (2.2.537) who has killed King Hamlet.
While scolding himself for his inaction, Hamlet finally has an idea upon which he can act. He recalls that guilty people have watched plays so cleverly presented that they are "struck to the soul" (2.2.554) by the drama, and their consciences are so profoundly stirred that they confess their crimes. This idea inspires Hamlet to have the actors "play something like the murder of my father" (2.2.558) so he can watch Claudius's reaction. Resolved that "the play's the thing" (2.2.566) and it will reveal Claudius's conscience, Hamlet moves on his plan. Once he has this proof, Hamlet can justify killing Claudius.
Earlier in this scene, Hamlet speaks with Polonius and pretends to mistake him for "a fishmonger." He acts as though he is mad, making absurd remarks. However, some of these remarks hide truths, and Polonius notices that there is a method to Hamlet's madness. Hamlet's pretense of madness rouses suspicions.
The soliloquy to which you refer is the "...rogue and peasant slave.." speech. Here, Hamlet is upset with himself because he's done nothing yet to avenge his father's death as he promised the ghost he'd do. At the beginning of the speech, he compares himself to the actor who, delivering the lines he just gave, was so emotional, he had tears in his eyes. Hamlet says he should be that emotional and determined to avenge his father's death. He says that he hasn't even done any planning and that if anyone were to call him a wimp or to slap him, he'd deserve it for his inaction. Then he rants about his uncle, calling him a "bloody, bawdy villain!" among other names. He becomes determined to take some kind of action and so, at the end of this speech, says he's heard that someone, seeing his bad deeds enacted, might react, therefore he'll have the players enact a scene depicting his father's death and see if Claudius reacts. That way, Hamlet will know that the ghost was indeed the spirit of his dead father and not a demon trying to lure him into hell by getting him to commit murder. Hamlet's earlier remarks to Polonius tell us that Hamlet has disdain for Polonius whom he considers a meddlesome person. Hamlet makes caustic remarks to Polonius reflecting Hamlet's scorn for Polonius.