In 1930, he became the first writer from the United States to be awarded the Nobel Pr

If the article was a recognised part of the name of something, then it would probably be capitalised.Eg :I'm reading "The Lord of the Rings" by JRR Tolkien

With something like the Nobels, no, because "the" is not part of the name - it's just an ordinary article. Compare :

He won a Nobel prize.
They don't give away Nobel prizes for nothing.
He won the Nobel Prize for Literature.

The article is used as it would normally be used depending on the sentence construction. It's not "part of" the name.

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The two aren't related. You're confusing names and titles. Strictly speaking, all the publications you cite have "the" as part of the name, and it should therefore be capitalised. However, this is what it says in the Guardian style guide under the entry for "the" (lc = lower case; uc = upper case)

lc for newspapers (the Guardian), magazines (the New Statesman), pubs (the Coach and Horses), bands (the Black Eyed Peas, the Not Sensibles, the The), nicknames (the Hulk, the Red Baron), and sports grounds (the Oval).

uc for books (The Lord of the Rings), films (The Matrix), poems (The Waste Land), television shows (The West Wing), and placenames (The Hague)

The Guardian Style Guide, though only a guide, is usually the best source to consult for questions like this.

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It's not a matter of "should" but of preference. The Style Guide is exactly that - a guide, ie suggestions for achieving a coherent, modern style. I'd suggest following it - but anyone is free to disagree. As I said above, there are reasons for arguing either way.

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