1. In Medea, Medea unquestionably has magical powers, but how much does she depend on them during the action of the play?
2. Trace the steps thorough which Medea's plan of action is carried out.
3. Compare Medea and Clytemnestra. Both are wronged wives who seek revenge.
4. In what sense is Medea a hero like Achilles, Antigone or Odysseus? What qualities does she have that may command our admiration?
5. In an alternate version of the story of Jason and Medea, Medea does not kill her children, but instead escapes with them safely tucked beside her in her dragon chariot. If Euripides followed that plot, how would your response differ?
I will answer a few of your questions here.
Like Circe, Medea is well-known for being a sorceress, but in this play she is less dependent on her magical powers than on her all-consuming desire for revenge on her faithless husband Jason. This motive for vengeance is what drives the entire play. It is true that she manages to effect her escape from Corinth by means of her magic powers, when she ascends in a chariot belonging to her divine grandfather, the sun-god Helios; with her dark arts she is also able to poison the robe she sends her rival, Glauce, but throughout the play her human passions, not her magical abilities, are emphasized. Her emotions become the real source of her power. The sensational events of the play, then, derive from recognizable human emotions - albeit emotions pushed to a terrifying limit - rather than from the working of any magical or supernatural agencies. It is a play concerned more with a psychological realistic depiction of its characters than with wondrous events. The emphasis is on Medea as a wronged and bitter woman, not as a sorceress.
Medea has recognizable traits in common other ancient Greek heroes like Achilles or Antigone in that she is a towering figure driven by extreme emotion. Achilles is distinguished by his wrath; Antigone by her passionate duty to her family. Medea is comparable to such figures in that she is propelled by her ferocious desire for vengeance. (Odysseus, whom you also mention in your question, differ somewhat from this group in that he appears less driven by overpowering emotions; still, like them, he too exemplifies a particular human trait: cunning.) Like Achilles and Antigone, Medea is driven to actions that appear extreme: the strength of her passion sets her apart from others, and cuts her off from normal human intercourse, but she is still recognizably human in her passions and desire.
Medea may be counted admirable in one sense: she refuses to sit back and tamely submit to the unfair punishments meted out to her. After all, Jason is the man for whom she dared everything, but he decides to reject her simply for his own selfish political gain, thus making a mockery of their personal relationship. Creon’s decisions to exile her further exacerbates the situation. However, she chooses to defy society, and specifically the men who dictate to her; she stands up for her rights as a woman – and it should be borne in mind that in ancient Greece, women officially had very few rights. Medea fights against this. She goes too far with the killing of her own children, but we can understand her actions even if we do not condone them. It is all the easier to understand her position as Euripides makes clear her predicament at the start of the play, when she eloquently pleads her case.
To consider your final question, surely for most readers the overall effect of the play would be considerably diminished if Euripides had chosen to end with the children escaping alive with Medea. The overwhelming impact of the play derives from its searing portrayal of a woman who will stop at absolutely nothing to wreak her revenge, and the murder of her children by her own hand adds considerably to this grim picture. Their killing, abhorrent as it is, also emphasizes the perfection of her revenge against Jason, who is left with nothing and driven to the last stages of despair.