What is the ruling on praying in a place surrounded by a fence that separates it from the graveyard by a low wall and has a door, knowing that there are other places outside the village, and that this place has become too small for the villagers?

The Eid prayer is permissible in the aforementioned prayer area as long as there is a barrier separating it from the graveyard. However, it is from the Sunnah (definition) to perform the Eid prayer in the open desert outside the village, as this is what the Prophet, peace and blessings be upon him, and the Caliphs after him used to do, because it is more impactful for the grandeur of Islam and more demonstrative of the rituals of the religion.