Is it permissible to say "upon him be peace and blessings" when mentioning the Prophet Muhammad, or should we say "may Allah bless him and grant him peace" or "O Allah, bless Muhammad and his family and companions and grant them peace"?

You are permitted to send blessings upon the Prophet, peace and blessings be upon him, using the mentioned phrase "peace and blessings be upon him" or other formulations, as the matter is broad. However, it is preferable in prayer to limit oneself to the established forms transmitted from him, peace and blessings be upon him. Sending blessings upon the Prophet is a great act of worship with immense reward, as the Prophet, peace and blessings be upon him, said: "When you hear the muezzin, say as he says, then send blessings upon me, for indeed, whoever sends blessings upon me once, Allah will send blessings upon him ten times." It is also prescribed to send blessings upon him when he is mentioned, based on his saying: "The miser is he in whose presence I am mentioned, and he does not send blessings upon me."