In other sentence it is written "Η γυναίκα τρώει ρύζι" (a woman...); but here it doesn't match "a woman...". Is it a mistake?
Are you sure it was η γυναίκα; Because η γυναίκα = the woman, while μια γυναίκα = a woman.
διαβάζει is the verb form for third person singular ("he, she, it" and singular nouns), and διαβάζουν is the verb form for third person plural ("they" and plural nouns).
Here, the subject is η γυναίκα "the woman" which is singular, so you need διαβάζει.