What is the ruling on performing Jumu'ah (Friday prayer), Tarawih (night prayers in Ramadan), and Eid prayers in a small musalla (prayer area) located four hours away from the nearest mosque, and is it permissible for one of the twelve worshippers to lead them in these obligatory prayers?

What you have done by establishing the prayer area (musalla) is good, for establishing congregational prayers, Jumu'ah, Tarawih, and Eid prayers therein. Congregational prayer for the five obligatory prayers is incumbent upon individuals. Tarawih and Eid prayers are permissible in this musalla, and Jumu'ah prayer is permissible therein according to the most preponderant opinion, because a mosque is not a condition for its validity according to the soundest view. There is disagreement regarding the number required for Jumu'ah to be established, but the soundest view is that there is no specific number required. The one who recites the Qur'an best and has the most understanding of fiqh should lead you in prayer. It is preferable to attend the mosque on Friday if possible, to avoid scholarly disagreement.