I guessed the third one based on a memory of a Peanuts comic, but I can't find it online.  Has anyone seen it?

What American author set most of his novels in the fictional Yoknapatawpha County?

What English poet wrote The Rime of the Ancient Mariner ?

What Austrian composer, known as the "Father of the Symphony" wrote 104 of them?

What last name is shared by a winner of the 1945 Nobel Prize for Medicine and a British author whose estate sponsors a prize for thriller novels ? 

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I'm guessing Faulkner, Coleridge, and Mozart. No idea on the last. Fleming?
Mozart is incorrect, but Fleming is correct.
Who was the composer frequently mentioned in Peanuts?

Hint: Lucy thought his first name was Lawrence.
Schroeder’s hero is Beethoven, but that’s not the correct answer to “Father of the Symphony” question. I can imagine this guy in _Snoopy’s_ thought bubble for some reason.
I knew 3 off the top of my head because of your hint, I couldn't remember 2 until I read it out loud, and then it popped up, and I didn't know the winner of the 1945 Nobel prize for medicine specifically, but after I read it all the way through, I was pleasantly surprised by that connection.

For 1, I thought, "some guy with a mustache who wears linen suits and smokes hand-rolled cigarettes or a pipe."
No one has yet taken me up on the $50 bounty for translating Faulkner's "Barn Burning" into Klingon. I say it's because the themes of honor and vengeance are aligned with Klingon culture, but it was also inspired by how much Yoknapatawpha already sounds like Klingon to my ear: https://osric.com/university/klingon.html

It's such an under-valued language.