As we have seen (above, section 8), the fast technically ends at tzeit, but since there is a mitzva to add to the sacred, we end the fast a few minutes later than that. In Eretz Yisrael, once thirty minutes have elapsed since sunset, it is already several minutes past tzeit, so one may make havdala, eat, and drink. It is not necessary to show concern for Rabbeinu Tam’s view that tzeit is seventy-two minutes after sunset (Peninei Halakha: Shabbat 3:1 n. 1).
Ma’ariv may be started twenty minutes after sunset, but to remove uncertainty, the first paragraph of Shema should be repeated after Ma’ariv (Peninei Halakha: Prayer 25:5).
Many recite Kiddush Levana right after Yom Kippur. The days leading up to Yom Kippur are tension-filled due to the upcoming judgment. Since Kiddush Levana must be recited joyfully, it could not be recited then. With the completion of the Yom Kippur prayers, however, our joy reaches its apex; it is thus an auspicious time to praise and thank God for moonlight. Some prefer to go home and eat and drink first, and then reassemble a minyan to recite Kiddush Levana joyfully. However, if one is afraid that he will forget or have a hard time finding a minyan later, it is better to recite it right after Ma’ariv. (See 5:7 above.)