"on the weekend" is simply the US usage, as seen here:
"at the weekend UK (US on the weekend): on Saturday or Sunday, or on both Saturday and Sunday"
Only if "w" is followed by another consonant, so "w Warszawie", "we Wrocławiu", "w weekend" and so on. There are two(as far as I recall) exceptions – always "we Lwowie" and "we śnie" even though they don't start with "w". Also, some people(but not all) say "we Środę" and "we Czwartek", but I think that is only accepted in colloquial speech.
Depends on what you mean by "recent" – it is commonly used for at least a century now – but the problem is, when rendered in Polish orthography, "weekend" is pretty ugly/awkward(either "łykend" or "łikend", both of which look disgusting to me), so despite being pretty old, it still doesn't have 'native' spelling. Some specialists even think it will never get 'native' spelling as long as English will be global language and many/most Poles will know it because of that, which is opinion I personally agree with.
Well, there are other factors too, like whether the loan in question is a synonym for already existing word or not; whether the term the loan word names/describes is popular or not and so on. All these factors led to very early full adoption of computer-related terms like "komputer", "mysz"(as computer input device) or verb "klikać" for example and most of these don't exist for 100 years even in English. ;-)
"Weekend" should really be in this category, but the spelling is still not native, despite the fact it has no real synonyms and most Poles use it at least once per week… ;-)
Well, for the young generation it's definitely something obvious ;) As I've read now, free Saturdays (in the number of two a year) were first introduced in 1973 and their number (in the year) was rising. In the 1980s there were some working Saturdays and some free Saturdays. And then after the fall of the communism, free Saturdays for the whole year began to be a fact.
You are correct about the meaning of your translation. Duolingo doesn't always think of every English variation. Although, a more direct translation in Polish also exists for your sentence.
Co będziesz robić w weekend? (I really dislike that Polish uses the English word!) :-)
In Ukrainian, Szczo budesz robyty w wychidni?
AT the weekend...or ON Saturday and Sunday... should also have said...'this' weekend. Sorry if my 70 years of born and bred English native speaker contradict 'on' the weekend...but AT the weekend is what it is...there are loads of possibilities (this weekend, during the weekend, will have it ready for the weekend, as well as at) to go with weekend, but ON is not one of them...