Native speaker might have a better explanation, but using 'til' before a time-noun is specific to when the time is still in the future and you are enquiring only about a coming event. So, 'til helgen' is specifically about this coming weekend.
'I helgen' can thus be more broad, and the question 'Hva gjør du i helgen?' might get an answer about what I normally do every/any weekend, but not only specific to this coming weekend.
My feeling (!) would be: to use 'til' when posing an open question, just being curious on what that person will be doing in the weekend to come. In contrast to the more directive question whether that person will go out this weekend, in which case I would use the 'i'. Besides this I would use 'om', to ask that person what he usually does during the weekend.
"Frem til" means "through to/until" (among a couple other variations) so potentially you could express your sentence with "Hva gjør du frem til helgen?"
But I'm not a native so this may not be the most accurate way to get the point across...! Hopefully someone can fill us all in?
The words for until are inntil and til, so I'd also be curious to know this. Perhaps the sentence above really is correct for "What are you doing until the weekend?" and they just haven't added it as an alternative translation. Confirmation from a native speaker and or contributor would be appreciated. ^_^
Oh that's interesting, I made a similar post a while ago complaining about "on the weekend", which I see is a phrase used by at least one of the mods but is not the way I hear or use it - it's always "at the weekend". Prepositions are unruly and illogical, and we never will understand them fully!