People go home or prepare to go to their work after Fajr prayer, except two days:
1) The first day of Eid Al Fitr, 1st day of Shawwal, the 10th month of the Islamic calendar (the first day after Ramadan)
2) And first day of Eid Al Adha, which is celebrated on the 10th day of Dhu al-Hijjah, the 12th month of the Islamic calendar.
were they stay in the mosque till Eid prayer performed.
Both prayers are performed after 15 minutes of the sunrise, and about 1 hour after Fajr prayer.