To be considered Jewsih is it your mother that must be Jewish and if so how Jewish, here mother alone was enough etc?
Yes, Jewish tradition bases their religion on the mother. You would have to go back every generation on the maternal side.
Yes, the child must convert as well.As far as I know (read) if your father is Jewish but your mother wasnt and converts the rabbis will still not acknowledge you (child) as Jewish. Infact so much so you cant get into a private Jewish school.