Othello 3.4

For the second time in the play, the Clown shows up. Just as last time, his role is to provide some comedic relief for the upcoming drama. Desdemona is in a conversation with him and she is asking for Cassio's house so that she can try and have him reinstated. The Clown doesn't know where he lives but he promises to go and look for Cassio. Ironically, in this scene, Emilia is questioning Desdemona on whether Othello is a jealous person, but Desdemona is completely caught up in love and believes that Othello has never had any jealousy in his body since his birth. Othello then enters the scene and at this point, he is overcome with jealousy. As a test, he asks where the handkerchief that he gave Desdemona is. Desdemona misplaced the handkerchief and Othello storms off the stage in anger. Cassio then enters and they have a small conversation about Othello's anger before Desdemona and Emilia leave to look for Othello. The introduction of Bianca follows after. Bianca is Cassio's secret lover who is head over heels for Cassio. Cassio tells her to copy the embroidery of Desdemona's handkerchief that was planted in the room by Iago. Bianca becomes suspicious of Cassio cheating but after a short conversation she is somewhat convinced otherwise and leaves.

I find the clown to be a very intriguing character. Even though it may seem like he is only there for comedic relief, I believe that he symbolizes more than that. The other time that he appears is 3.1 where he is with a group of musicians outside of Othello's house where Cassio is trying to regain. Coincidently enough, Cassio at the time told the clown to fetch Emilia, who after assuring Cassio, invites Cassio in to talk to Desdemona alone. In both cases, both Cassio and Desdemona meet because of the clown. The clown represents a unique connection that Cassio and Desdemona have with each other.

Why does Shakespeare decide on introducing Bianca so late into the play?
Shakespeare introduced Bianca now instead of before for dramatic significance. Bianca's role in the play is primarily as a Cassio's proof of loyalty so far. With some of the actions and words of Cassio, the audience could be convinced that Cassio had something to do with Desdemona, but with the introduction of Bianca, the audience knows that Cassio is the full victim of Iago's plans. 

http://www.arogundade.com/the-handkerchief-in-william-shakespeares-othello-handkerchief-scene-symbolism.html
The article goes into a lot of details into about the handkerchief. The author mentions details about the medieval significance of the handkerchief as well as the dramatic significance of a turning point. The article is easy to understand and provides a detailed analysis of 

How are Desdemona’s words in lines 31-32 ironic?

Desdemona’s words are ironic because she says that Othello isn’t a jealous person, but Othello is extremely jealous.

If what significance is the handkerchief to Othello (the character, not the play)? What new insight does this give to his character? Is this surprising to you?

The handkerchief is a momento of Othello’s mother and it is significant in how his mother put meaning in it. Othello’s mother believed that the handkerchief is the reason why she is lovable and Othello adopts this thinking showing that he is somewhat superstitious.

Why must Iago take his time to convince Othello about Desdemona and Cassio?

Iago has to take his time because otherwise, it would seem like he is intentionally trying to create tension between them. By seeming reluctant and hesitant, he makes Othello believe that he is good-natured and hurt to tell Othello.

Explain the importance of Desdemona’s handkerchief (to the play).

Desdemona’s handkerchief is the ignition for the chaos that is about to happen. Even though the handkerchief is supposed to be a loving act from Othello to Desdemona, it becomes the object of jealousy for Othello.

What role does Emilia play in Iago’s plot?  Explain specifically.

Emilia’s role in Iago’s plot is something similar to a spy. She provides information about the couple to Iago and occasionally plays a vital role in stealing something. Her status as Desdemona’s servant allows her to be close.