Is it permissible for a woman's parents to give her Zakat if her husband is absent and she lives with them? And is it permissible to give Zakat to a sister?

A daughter is not given Zakat unless her parents are no longer obligated to financially support her. This obligation is lifted in two cases: her marriage, or if she is an adult capable of earning a living. As for a sister, there is no impediment to giving her Zakat if she is eligible to receive it.