Without looking at any comments or other answers:

Bismarck is the capital of North Dakota.

If I went to the place identified as "Bismarck, North Dakota" on widely-used maps and looked around, I would see a building where some folks calling themselves the North Dakota legislature were prone to meet and talk in a formalized way about North Dakota law. Their deliberations would be reported on in newspapers that could be found in many towns in the area described on many widely-used maps as "North Dakota".

The universe does not exist; all existence is imaginary.

This seems to be false by definition, since "imaginary" refers to thoughts or ideations that are distinct from everyday life. The only data we have for distinguishing "the imaginary" from "the not-imaginary" are within the universe.

The earth is flat.

If I synchronize two clocks and send them to different points "around" the earth, observers will see the same angles of shadows at the same clock times.

The comic book Queen & Country is based on the British ITV series The Sandbaggers.

First: I can find the comic book and TV series mentioned in resources that describe other such things. Second: There are similar characters, plotlines, or settings between them, according to a notion of "similar" that I'm not actually prepared to analyze right now.

Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is a good book.

People who read it, drawn from some reference class I'm not prepared to analyze right now, are not disappointed.

"A Visit from St. Nicholas" (a.k.a. "Twas the Night Before Christmas") was written by Clement Clarke Moore.

If I go to the library and look it up, I get results that agree with the proposition. Standard references express less disagreement on the matter than on the authorship of Shakespeare's plays, since Clement Moore is more recent.

Herbert Hoover was left-handed.

Museums likely to have artifacts from Herbert Hoover's administration include writings written with left-handed penmanship styles, or have specific instruments such as scissors in left-handed orientation.