Learn French: Quelqu'un cache une trace ou une preuve. - Someone is hiding a trace or a proof.

Because quelqu'un means "someone", it acts as a third-person singular subject, exactly like il (he) or elle (she). That is why the regular verb cacher (to hide) is conjugated as cache here.

Why is there an apostrophe in quelqu'un?

It is a combination of quelque (some) and un (one). The letter 'e' from quelque is dropped and replaced with an apostrophe to avoid having two vowel sounds right next to each other, making it smoother to pronounce.

Do I have to say une twice in this sentence?

Yes. While in English you can just say "a trace or proof", French grammar requires you to repeat the article (like un, une, or le) before almost every noun, even when they are joined by ou (or).

Does une preuve mean "proof" or "evidence"?

It means both! While une preuve translates directly to "a proof", it is also the most common way to say "evidence" or "a piece of evidence" in French.