In act III, to whom does Cassio appeal for help in regaining his position? What does Othello say he plans to do with Cassio?This is in act 3!
In this scene, Cassio responds to Iago's earlier prompt that he should consult with Desdemona in order to gain Othello's favor. Iago told the naive ex-lieutenant that he would be assured of receiving a friendly hearing from the general since Othello would be easily persuaded by his wife because he loved her so much.
Cassio tells Iago that he took courage and asked Emilia, Iago's wife and Desdemona's waiting-lady, to arrange a meeting with the general's bride so he can urge her to help him. Iago, who obviously wants to control the situation, tells him he will send Emilia to him.
When Cassio later meets Emilia, she informs him that the general and his wife are already discussing the matter and that Othello has stated that the person Cassio hurt in their earlier brawl (Montano) is greatly respected and loved in Cyprus and that the general, in wise consideration, must refuse Cassio's appeal for re-appointment. This would obviously be the politically correct route, since Othello does not want to create the impression that he disregards Montano and the offense Cassio committed against him. To do so could possibly lead to the general falling into disfavor. Othello has stated that he still has much affection for Cassio, and will consider reassigning him as soon as it is safe to do so.
Cassio later meets with Desdemona, who assures him that she will do her best to defend him and seek his reappointment. When Emilia informs them of Othello's arrival, the two part. Iago, who is with Othello, makes it appear as if they had been doing something illicit and that Cassio slunk away like a thief.
Othello's curiosity is aroused, and he demands to know what Iago is implying. From this point onward, Iago manipulates the general into thinking Desdemona and Cassio might be having an affair. When Desdemona asks Othello about Cassio, he is very dismissive and quite rude. He develops a headache and when Desdemona tries to help, he pushes her hand away from his brow, making a handkerchief he gave her as a gift fall to the ground.
Emilia picks up the handkerchief and gives it to Iago, who later uses it as a tool to manipulate the general. Iago convinces Othello of a supposed affair between his wife and Cassio by referring to statements that Cassio made and the handkerchief that Iago purportedly saw in Cassio's possession. The general promises vengeance.
At the end of Scene 3, Othello asks Iago to kill Cassio within three days. He says he will take care of Desdemona. He then appoints Iago as his lieutenant.
Cassio's method for seeking help reveals his utter powerlessness. He tells Iago at the beginning of Act 3 that he has sent to Emilia (Iago's wife) to help him gain access to Desdemona, who he hopes will help him gain access to Othello. Cassio was the "go-between" when Othello and Desdemona were first seeing each other, so Desdemona feels that both she and Othello owe a debt of friendship to him and she is more than willing to pay it by asking Othello to reconsider. Emilia tells us that Othello is already predisposed toward helping Cassio, but that for political reasons he must wait for the time to be right because the man Cassio hurt was well-regarded in Cyprus. Yet when Othello agrees to meet with Cassio, he says he does it to stop Desdemona's mouth, and he does it as a "boon"-a favor-to Desdemona.
Cassio appeals to Desdemona to help him regain his position. Desdemona tells Cassio that she will do all she can to help him. Iago then, of course, uses this to show Othello that Desdemona and Cassio are having an affair. I'm not sure what you mean by the begninng of the act, however in the beginning of Act 3 scene 3 Othello says he’ll give Desdemona what she wants, and talk to Cassio and asks to be left alone.