Which is better: praying in the mosque or at home, given that the imam makes mistakes in reciting Al-Fatiha, and knowing that the worshiper desires congregational prayer due to its virtue, and he resides in a foreign country?

If you are certain that the Imam commits a clear error in Al-Fatihah by changing one letter for another, then following him in prayer is not valid according to the majority of scholars. The Imam must be taught the correct pronunciation and guided. If that is not possible, then someone else should lead the prayer. If all of this is impossible, and you pray with him, imitating those who consider following him valid, then there is no harm. However, if you pray in your home as a congregation to avoid the disagreement, that is good. But if it is merely a whisper (waswasah) regarding the articulation points of letters, do not pay attention to it.