Is it obligatory to say the Basmala before cleaning a live fish that was slaughtered by striking its head and opening its belly, and is it a condition that this be done by a Muslim?

Slaughtering (Dhakah) and the pronouncement of Allah's name (Tasmiyah) are not required for fish, because Allah has permitted the dead creatures of the sea. The proof for this is the Prophet's (peace be upon him) statement regarding seawater: "Its water is pure and its dead creatures are lawful." Thus, it is permissible to eat fish even if caught by a disbeliever whose slaughtered animal is not lawful.