What is the title and rank of St. Michael amongst all the Angels and exactly what is or was his responsibility?
The most appropriate mythological title from a historical source POV would be "Jewish Prince of Heaven who was once the Babylonian King of Hell."
The Archangel Michael is copied in both name and attributes from sources around at least 1600 BCE, a thousand years before he is ever mentioned in Judaism. He found his way into Hebrew via the Babylonian Exile in the fifth century BCE, and through neighbouring West Semitic cultures where he was a prominent chthonic martial deity called Mikal.So like many angels, Michael is a holdover from polytheistic times.
Mikal’s name came from an Akkadian word for “red” which was a poetic name for the planet Mars. This name was a title for both the Sumerian god Nergal (with whom Mikal was syncretized) and got taken by the Babylonian god Marduk as a result of the conquest of Sumer. The name is distinctly Semitic and the deity follows distinctly Canaanite mythic tropes.
Mikal was a warrior god of thunder, portrayed in full battle gear much like Michael is today. Unlike Michael he had a consort; the warrior goddess of love and sex, Anat.
Mikal was the giver and taker of plague, and god of the underworld. He was the lord of the underworld and synonymous with the Babylonian god Nergal, who was the planet Mars, from whence Mikal got his name. The color red, especially in candles, is still canonically associated with the Archangel Michael to this day.
There are no explicit references to archangels in the canonical texts of the Hebrew Bible. In post-Biblical Judaism, certain angels came to take on a particular significance and developed unique personalities and roles. Though these archangels were believed to have ranked amongst the heavenly host, no systematic hierarchy ever developed.
The New Testament makes over a hundred references to angels, but uses the word "archangel" only twice, at Thessalonians 4:16 ("For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first", KJV) and Jude 1:9 ("Yet Michael the archangel, when contending with the devil he disputed about the body of Moses, durst not bring against him a railing accusation, but said, The Lord rebuke thee", KJV).
However, further proof of the Babylonian origin of Michael can be found in the oldest surviving forms of Christianity, such as the Coptic church, where his name is Ramuel, meaning "Thunder of God".