Does the Friday prayer fall away from whoever witnessed the Eid prayer if Eid and Friday coincide, or is this ruling limited to the people of villages, and is this opinion acted upon in our current era?

If 'Eid and Friday coincide, the Madhhabs of the Hanafis, Malikis, and Shafi'is hold that one prayer does not suffice for the other. However, the Shafi'i Madhhab grants a concession to villagers who attend the 'Eid prayer, allowing them not to attend the Friday prayer.

As for the more preponderant view (al-Madhhab al-Rajih), which is authentically transmitted from the Prophet (peace and blessings be upon him) and the Companions, it is that whoever attends the 'Eid prayer is exempt from the Friday prayer. Nevertheless, the Imam must still hold the Friday prayer for those who wish to attend it or who did not attend the 'Eid prayer. Whoever does not attend the Friday prayer should pray Dhuhr. If only one person is present with the Imam, they should both pray Dhuhr.