Irregularities like this are unfortunately somewhat common in Esperanto. (See the lessons on countries/nationalities.) Zamenhof, being an opthalmologist and not a linguist, did not seem to consider not everyone would be interested in needing to learn the etymology of certain words in order to use them correctly.
For all the confused esperanto speakers, how does esperanto say "one sheet of paper"? It might not be a torn off piece, but it is still a specific amount, not the unspecified amount in the question. The sentence in the question would be asking for multiple sheets at least as often as asking for a single one.
No, the '-n' ending is only for direct objects, not indirect. In other words, if there's a preposition (like "en", "por", "al", "kontraŭ", etc.) then you don't add the '-n' to the following word.
To put it another way: when you've got two Things in a sentence, you need to mark one of them as the subject and the other as the object (the "do-er" and the "receiver of the action"). The unadorned noun in Esperanto is the subject, while the object needs to be marked either by a preposition or by the '-n' ending.
Hope that helps.
After reading other comments on this sentence, I'm still not clear on the meaning of "papero". Is it only a single sheet of paper, as the provided translation suggests, or can it also mean the substance, or uncountable noun, paper? Can it in addition mean a paper as in a written piece of text (e.g. a submission to a conference, or an essay to be marked)?
I read the last two posts, however I still have a question. would 'Ĉu vi havas pecon da paperon por mi? be incorrect? To me "Ĉu vi havas paperon por mi? Sounds like a snarky prof asking if you have your paper to turn in, Or you're at a news stand, and are asking for a newspaper. I guess I'm still unclear on why "pecon da" isn't used.
It's just your English-speaking sensibilities telling you it needs to be "a piece of" paper. What the others are saying is that in Esperanto, it's only "pecon da" if you've removed a portion from a whole. If you tore off a corner, that would be "pecon da papero". But one single sheet of paper is whole unto itself. Think of it this way: We don't say "a piece of grape" even though they come in bunches. We only say "a piece of banana" if we want a portion of one.