1. What night did 1 Av 5778 begin? Thursday night? Friday night?
2. When you see the number for the Jewish day on the calendar, does that date, for example Av 1, begin [ON THE CALENDAR] that evening, or does it reflect the day, of the Jewish month, that began the night before?
1. Thursday night
2. It reflects the day. Think of shabbos if that helps. Your claendar labels the seventh day of the week as Shabbos. But you know that in actuality it begins Friday night. If your calendar says Tisha ba’v is Sunday that means it begins Saturday night, the same is true for any day including Rosh chdesh or 1 Av. (with chanukah in particular this can be confusing your calendar probably says Monday 12/3 is the first day of chanukah, though this means that on Monday 12/3 you will light 2 candles,)
Don’t get confused- This year your calendar will say that Tisha BAv is on Sunday, which is actually 10 Av. Since 9 Av is on Shabbos, when we do not fast/mourn, the fast is pushed off 1 day to Sunday.