A valid translation for this, IMHO, would be "Arts or science?" At least that was how my school was divided.
Well, "arts" is 'sztuka'. I don't think the author had something specific in mind. Or just the Palace of Culture and Science ;)
I don't think this is a complete sentence. I would not use a question mark for this exercise.
"A or B?" seems like a normal question to me, which one you prefer.
Of course, normally it's put in some context.
Where is the verb in this sentence or question? Are you telling me, I don't need a verb to make a sentence? "Or" is a conjunction.
"Paper or plastic?" is, or at least, used to be, a perfectly valid question in US supermarkets at the checkout. The rest of the question "Do you want..." can be inferred by the listener.