Is a man's prayer with his wife considered a congregational prayer (salat al-jama'ah), what is its virtue compared to praying in the mosque, and are there prayers that can only be performed in the mosque?

A man's prayer with his wife is considered a congregational prayer, because a congregation is formed by two people. However, the merit of congregational prayer, which is 25 or 27 degrees, is specific to the congregation of the mosque, as indicated by Al-Bukhari. This is supported by the prophetic tradition that links the multiplication of reward to going out to the mosque. The difference between congregational prayer at home and in the mosque is that congregational prayer in the mosque is obligatory according to the stronger opinion, and the mentioned merit is specific to the mosque's congregation, although congregational prayer at home also has merit, even if not specified. As for other prayers in the mosque, they include Tahiyyat al-Masjid (greeting the mosque prayer), supererogatory prayers (preferably performed at home), Tarawih prayers, and Kusuf (eclipse) prayers.