When did they resume building the Bayis?
Rashi: After Koresh, Achashverosh ruled, and then his son from Esther 1 , Daryavesh (Vayikra Rabah 13:5). From Koresh's first year until Daryavesh's second year were 18 years, to complete 70 years from Churban Yerushalayim. There were 52 years from Galus Tzidkiyah until Koresh's first year, like it says in Seder Olam.
Esther continued intimacy with Mordechai after Achashverosh took her (Megilah 13b). We require Havchanah (abstention, if needed to evade a Safek about who is the father)! Tosfos (ibid.) says that she used a Moch (wad) to avoid pregnancy from Achashverosh. After she separated from Mordechai in Achashverosh's 12th year (ibid. 15a, Esther 3:7), there was no more need for a Moch. If Daryavesh was born after this, he was at most two years old when he became king! Perhaps she did not use a Moch when Achashverosh first took her five years earlier (ibid. 2:16), and became pregnant then. She used a Moch afterwards, and returned to Mordechai after waiting three months. (PF)


