Is a Muslim sinful if he does not lead the prayers in his village, knowing that he is proficient in Tajwid and capable of leading, and the mosque does not have a permanent imam, and most of the villagers do not recite Al-Fatihah correctly?

The precedence of the most proficient in recitation for leading prayer is recommended, not obligatory, just as some aspects of Tajwid are obligatory and others are recommended. A person is not sinful for relinquishing imamate to someone less proficient in Tajwid, as long as the recitation of Al-Fatiha is correct.

However, if the one stepping forward to lead the prayer cannot recite Al-Fatiha correctly, and there is no one else to lead the people, then leading the prayer becomes obligatory upon you, and you would be sinful if you do not step forward, or if the matter is not referred to the Ministry of Endowments to appoint an Imam.