Its only high on the west coast. That's because of multiple complicated reasons. Basically the west coast is an independent energy zone from the rest of the US. And California (where most of the refineries are for historical reasons) hasn't made very informed choices with its energy policy. Also, the oil they use comes from abroad while the oil in the rest of the US comes from domestic sources and the rest is exported. Also, there isn't a lot of heavy sour crude in the world and that's the type of oil that yields the most diesel.

There is a lot more to it, but its too complicated to explain in a post.

I can't speak to whether or not we have excess diesel, but the price would be high because U.S. diesel is sold outside of the united states, so if EU members are willing to pay higher $$$ for it, then that's what U.S. oil producers will sell it for, raising domestic prices in turn.

If you cannot export it because of a ban, you would have excess diesel yes. Assuming you keep refining at the same rate as demand for the other products hasn't gone down