A weekly feature of Torah Tidbits to help clarify practical and conceptual aspects of the Jewish Calendar, thereby better fulfilling the mitzva of HaChodesh HaZeh Lachem...
As mentioned in last week's TT, the molad of Tishrei is before noon on MON, which would usually mean that RH would be MON (and TUE), but that would result in shortening 5765 to 382 days, which cannot be. Therefore, the very rare D'CHIYA (postponing rule for the fixing of RH) is applied, and RH is fixed at TUE (and WED).
Minhag Yerushalayim is to say Kiddush L'vana as soon after 3 full days after the molad as possible. Even in Tishrei, when the most common custom is to wait until motza'ei Yom Kippur for KL. First op for Minhag Yerushalayim is THU Oct. 6.
Because THU is a fast day, it is proper to say KL only after breaking one's fast.
As mentioned, most people/shuls wait until after Yom Kippur. In that case, it is not necessary to say havdala and break one's fast before KL.