Does Catherine deserve any blame for Eddie's feelings towards her?
Catherine is a teenager and has grown up with Beatrice and Eddie as her parents. She has not seen much of the world and is just experiencing what it feels like to be a woman. Given all this, she deserves absolutely no blame for her role in Eddie's obsession. He, on the other hand, is an adult, and he manipulates and preys on someone who is essentially a child. However, Catherine does give Eddie signs that encourage his attention, and here Miller complicates our moral sense of the two characters. Beatrice tells Catherine she must stop walking around in a slip and sitting on the edge of the bathtub while Eddie shaves in his underwear. Even the most naive teenager might realize these things on her own, it seems. Furthermore, Catherine gives a strange speech criticizing Beatrice for not being a good wife to Eddie and insinuating she does a better job of taking care of him. It is certainly likely that Catherine knows what she is doing to an extent, and even though Eddie is still in the wrong, his feelings are somewhat understandable.
What makes Eddie a tragic hero?
Eddie is a classic tragic hero. He is an Everyman trying to live his life while burdened by a terrible secret and a terrible flaw. His love for Catherine and his inability to recognize it for what it is lead to his downfall. As Alfieri points out, this downfall is almost inevitable. Eddie can no longer look at himself perspicaciously; he cannot change or grow or deviate from his path. He does not achieve redemption and dies at the close of the play. However, despite his stubbornness and immoral love for Catherine, he retains some sympathetic qualities which also add to his status as a tragic hero; he is no villain whose comeuppance we yearn for. He is a regular man suffering from a tremendous guilt and burden, and his death is sorrowful.
Why is the play's setting important?
While the psychosexual tension, repression, and violence of the story are universal (indeed, there are multiple parallels with Greek tragedies), Miller chose to set his play in his own era: 1950s America, in an immigrant population in Brooklyn. He does this to 1) assert the working-class nature of the protagonist, which exacerbates some of the tensions regarding Rodolpho "stealing" Catherine 2) delve into a population already marginalized by xenophobia 3) call attention to the persecution of supposed communists, which led to snitching and rumormongering. He makes us question the values of American society while presenting his universal drama.
How would you characterize Beatrice's relationship with Eddie?
Beatrice is a beleaguered character if there ever was one. She watches her husband fall in love with her niece, stop sleeping with her, fall into rages/sulking/despair/violence, and utterly repress any true self-knowledge about what is going on. He even blames Beatrice for their marital problems and demands that she respect him more. However, in the end, all of her sharp words and accusations and cries of frustration are muted by her choice to stay with Eddie instead of going to the wedding. There are many speculations as to why she does this. She may truly love Eddie despite all he has done; she may fear the wrath of her community if she violates gender norms by leaving her husband; she may fear the loss of any economic security if she leaves. Whatever her reasoning was for staying with Eddie it is to no avail, for Beatrice still finds herself alone at the end of the play.
Why is Eddie so distrusting?
Throughout the play Eddie expresses profound distrust of almost everyone he meets or knows. He says that the women cannot trust anyone to keep the secret about the immigrants. He does not trust men with Catherine. He does not trust Rodolpho. All of these examples are no doubt projections of Eddie's tormented psyche: he does not know himself or trust himself with his true feelings regarding Catherine and/or his potential homosexuality. Somewhere deep down he knows he is living a lie, so it is only natural that he projects that outward and assumes everyone else is full of secrets and subterfuge.