Can you ask two questions in one sentence?

So I’m constantly trying to improve my grammar and punctuation, but one thing that’s “getting me” right now is whether you can ask two questions in one sentence. Here’s an example if you don’t know what I mean…

Should we go on SRK or GFAQs?

Should we go on SRK? Or GFAQs?

Which is the correct way to ask a question in this context?

Well, the “More Correct” one, punctuations and all, is the first one. Because sentences are meant to be read whole. So asking the second one seems like If I read the second sentence by itself, it just says “Or GFAQS?” which is kinda weird.

But of course, Asking it the first way also means you are limiting the choices between the Two.

Asking, “Should we go on SRK?” Is like asking, “Should we or should we not go on SRK, and why yes or no?”

It depends on why you’re asking the questions…