The reason the “angel” is surrounded by a rainbow, exactly like the rainbow surrounding God’s Throne in both Ezekiel (Ezek. 1:28) and Revelation, is that He is actually Jesus, in His capacity as messenger and preacher. (Remember, “angel” means “messenger.”)
Jesus appears as the seventh messenger because that is the number of fullness; He brings God’s full message and presence.
The guy in Daniel 10-12 is the same figure we saw at the beginning of Revelation. Daniel saw a figure he describes as “the likeness of a son of man”, clothed in linen like a priest, wearing a golden belt, “And his body was like the chrysolite, and his face as the appearance of lightning, and his eyes as a burning lamp; and his arms, and all downward even to the feet, like in appearance to glittering brass; and the voice of his word like the voice of a multitude.” Compare this to Rev. 1:13-16 and to this part of Rev. 10, and you’ll see it’s the same guy, and that the Book of Revelation explicitly tells us He’s Jesus.
This person in Daniel proceeds to prophesy about all sorts of things that must happen, including precisely how long Israel must wait until the Messiah comes and the dead rise (as happened at Jesus’ Resurrection):
“And many of those that sleep in the dust of the earth, shall awake: some unto life everlasting, and others unto reproach, to see it always… But you, O Daniel, shut up the words, and seal the book, even until the time appointed…”
This figure is called the Son of Man, and it was recognized by ancient Jews as combining both the prophesied features of the Messiah and the Biblical attributes of God. That is why Jesus called Himself “the Son of Man” during His ministry, and that is why such a seemingly innocuous name set off a lot of Pharisees and Sadducees so badly. (Normally, a “son of man” or “son of Adam” just means, “Male human,” and God calls all sorts of people “son of man” as a form of address from God to human.)
As Beatus of Liebana says in his commentary:
"“And I saw,” he said, “the strong angel descending from heaven, clothed in cloud.” He is the Lord, clothed in the Church, always being born to God out of the Church. But he is described as robed in the Church by diverse modes: now in a robe to the ankles, as we read at the start of this book; now in a white woolen cloak, as by Daniel (cf. Dan. 1:13); now with “cloud.” For we read “with clouds” as “with the saints,” as we read it by Isaiah: “Who are these who fly like clouds?” (Is. 60:8) And so he is in spiritual clouds, and in the holy Body.
“And the rainbow was over his head.” The “rainbow” is the promise of perseverance, (cf. Gn. 9:12-17) for he describes the Church in the Lord.
“And his face was like the Sun, and his feet like columns of fire.” Here is the great reason… [that John] told us before this, at the start of the book, that His feet were “on fire,” and [that] afterwards he said that His face shone, so as to show Him “on fire” in His suffering in this world, and shining out in the Resurrection. But now, he first says that His face shines and then that His feet are like columns of fire; so as to show how much bright excellence will be on the Church through Her suffering."
The seven thunders that reply are “thunders” because that is associated with the presence of God (Exodus 19:16), and there are seven to represent either the seven spirits (who represent the fullness of the one Holy Spirit, since seven is a number of fullness) or the seven churches (who represent the one Holy Church, since seven is a number of fullness).
His feet stand on both the land and the sea because He is preaching to everyone. To preach like a lion roaring is to preach strongly. (The lion is also associated with “a voice crying out from the wilderness,” as in St. Mark’s Gospel, and with the Lion of Judah, Who is Jesus also.)