Is the phrase "Naji the Prophet, upon whom be peace and blessings" unlawful, and is saying, "O Allah, send Your blessings upon you, O my Master, O Messenger of Allah, take my hand in my helplessness, reach out to me, O Messenger of Allah" permissible, and if it is permissible, how can the Prophet, upon whom be peace and blessings, reach out to the supplicant?

Munajat is a private conversation.

It is not permissible to supplicate to the Prophet, peace be upon him, as it involves shirk (polytheism). Allah is the Owner of all dominion, and in His hand is all good. He commanded us to supplicate and promised to answer: "And your Lord said, 'Call upon Me; I will respond to you'." (Quran 40:60). The Messenger of Allah, peace be upon him, advised: "If you ask, ask Allah; and if you seek help, seek help from Allah."