Should Rabbanim be teaching girls and women?

What are the pros and cons of a man teaching girls/women?
If a Rav teaches girls/women, should there be a Mechitza? What if the Rav is not married?
Can/should a Rav call female students by first name or a nickname?
What Gedarim should a Rav institute for himself when teaching girls/women?
How does the relationship a Rebbe has with his male students compare to that of his female students?
Are there topics that women should not be teaching, like Halachah?