Does the plural “let us” (Gen 11:7) indicate that God was speaking to some other spiritual beings, or what?

This is not altogether clear, but see comments on Gen 1:1 above for some notions. In this case, a significant possibility is that God was accompanied by assistants around the time that he punished the evildoers to confuse their language, as when two angels were with him before he destroyed Sodom and Gomorrah (Gen 18-19), and when “the destroyer” (Ex 12:23) slew the firstborn of Egypt. This is the sort of detail that the Bible might well leave to implication and inference, because the fact did not merit direct statement.

In confounding human speech (Gen 11:7), is God not doing something he temporarily undid at the Pentecost?

Yes. At the Pentecost, “they were all filled with the Holy Ghost, and began to speak with other tongues.” (Acts 2:4) It was then that “devout men, out of every nation under heaven” (2:5) heard the speech and wondered. In fact, many nations are listed, and people present from those nations did “hear them speak in our tongues the wonderful works of God.” (2:9-11) This was precisely the opposite of what happened at Babel, where God confused languages to prevent the accomplishment of the vain and ultimately (in this case, anyway) evil works of man.

How did God accomplish the scattering abroad from Babel (Gen 11:8-9)?

At least part of the answer is that God confused the language of the inhabitants of Babel. But that just raises the question how he did that, too. How he accomplished these ends, we are not specifically told and there is no way to know for sure. But we should bear in mind that God often accomplishes things through unwitting human agents. It seems to me that, if this was the first city and tower of the post-Flood world, and if they told themselves they would make a name for themselves and reach to heaven, they had grand ambitions, as Moses would have known the Babylonians did have. Different men might well jockey for position as leader; and one might well get the notion of using different words for things, as signs of allegiance and as a secret code indecipherable to enemies. Thus ambition would lead to speaking in competing codes; as a result, trust would evaporate and work would stop. The scattering would come when the people began to view each other as not just rivals, but as dangerous enemies. And that is just what we might expect of Noah, who was still on hand if all of living humanity were united, and his more decent offspring. They certainly would not trust the likes of Ham, Canaan, and especially Nimrod. Moreover, Noah might tell the people that God intended that they split up and go their separate ways. But, of course, this is all purely speculative. Again, we simply do not know.

In what sense does the text strongly imply that were they were “scattered” (Gen 11:8-9)?

Again, we have already been told that in Peleg’s day “was the earth divided” (Gen 10:25), implying that they were not divided into nations before that (see the question about “they” in 11:2, above). If so, this strongly implies that they migrated from Babel to the homelands that came to be associated with each nation, Mizraim going to Egypt, Japheth going to Greece, etc.

How and why did they “leave off to build the city” (Gen 11:8) of Babylon?

Indeed, since the city was Babylon, was the city construction temporarily halted, only to begin again later, or what? Probably what is meant is that the “city” then being planned, because it would include all people then alive, was going to be far greater and more splendid than the one that emerged, which included (perhaps) only Nimrod and his followers.

What is the significance of the name “Babel” (Gen 11:9)?

The name, בָּבֶל or Babel, might well be derived from בָּלַל or balal, which is glossed “mingle, mix, confuse, confound,” since the text explicitly states that the city was called Babel “because there the Lord confused the language of the whole earth”. The implication is that the future Babylon—which would have been well known to Moses—had roots in this city founded on the “confusion” wrought in their defiance of God.