Is it permissible to visit the shrines and mosques in Turkey and supplicate there? And are those who do so only the Ethiopians (Habashis)? What is the religious ruling on that and on marrying them?

Marriage to someone from the Habashi group is impermissible, as they are among the misguided sects. Their religion is not approved, especially since it contains innovations that lead to disbelief. Travel for the purpose of worship is not permissible except to the three mosques: Al-Masjid Al-Haram (definition), Al-Masjid An-Nabawi, and Al-Masjid Al-Aqsa. It is not legislated to travel to the shrines of saints or to supplicate there, as that is among the innovations that the Salaf prohibited. One must be wary of associating with people of innovation, for fear of corrupting religion.