Rosh Hashanah 20: Calendar Manipulation

Ulla traveled from Eretz Yisrael to Bavel, and he told the Babylonians how the Beit Din in Israel had added a day to Elul, which would insert a weekday between Rosh Hashanah and Shabbat, which would be so great for them in Babylonia. The questions are: why having that extra day would make a difference, and why especially in Bavel. Also, how are those witnesses treated? Namely, a process of intimidation that was employed judiciously, based on how the court wants the date to fall out, with regard to the holidays. Plus, when the witnesses are encouraged to lie (or close). And how the pattern of the length of the months falls into place (29.5 days needs to shake down to months of both 29 and 30 days, plus 4 extra days). Plus, defining the molad.