How can I describe Medea as a mother, a child killer, a sorcerer, and as a woman, and how can I describe her aims?
It is very hard to read this play and remember that the audience is supposed to cheer on or at least feel catharsis with the end of the play. I think you can find the answers to your question by considering her major speeches in each act. At the opening of the play she speaks eloquently about her past relationship with Jason and how she feels about marriage and Jason's betrayal. This reveals her womanhood. When she reveals her plan to kill the children as the ultimate revenge we see the cold-hearted child killer side of her, but in her subsequent scenes she gives some compelling thoughts about how killing her children herself is more merciful than having her enemies kill them in retaliation for her killing of the princess, Jason's new bride. She also does waver in her determination to see the awful act through. In regards to her sorcery, it makes her dangerous and seen as a threat, but it allows her to have the last say in her fate. She uses it to win Jason in the first place, to ensure an ally and safe haven with Creon in Athens, and her "connections" allow her to make her safe getaway in the end. She will not allow her reputation to be brought low. The salvation of her pride has always been her ultimate aim.
What a great question. Medea is a terrifying figure and the very fact that the ancient Greeks portrayed her as a witch tells us something. In short, the Greeks slant her in a negative way right from the beginning. A more interesting perspective is the view of Ovid, the Roman poet. He knows the ancient tradition and stories of Medea, but he portrays her in a much more sympathetic light. I highly suggest you read the section on Medea in Ovid's Metamorphoses - book 7. These lines show the agony of Medea. She actually has a voice and we can see that she is gripped with love, longing guilt, loyalties, etc. Also when we realizes that Jason later scorns and betrays her love, she acts in a certain way. Is this right or wrong? Whatever the answer is, there is always a context. And this context will give you enough information to form a sophisticated argument.
I don't know how I would categorize Medea as a mother. I was told that she killed her children to spite their father. So in light of that any woman who would do any thing to her children because she is upset with their father really didn't want to become a mother in the first place. It's very hard for me to believe that she actually wanted children to begin with.