Could you help me with pronouns in the examples below?

1] A pronoun's antecedent is the [pronoun itself or gender of the pronoun or word that the pronoun refers back to?

2] Which of the following shows correct pronoun/antecedent agreement: Everybody will need their books for class or Everybody will need his or her books for class or neither or both?

3] Which of the following shows correct pronoun/antecedent agreement? Each of the women carried their purse or Each of the women carried her purse?