"When are you free?"
Sorry for the late response and I can't reply directly, but regarding why「いつ」is a noun in Japanese: I honestly don't think I can answer that. All I can say is that this is just another case of grammar differences, Japanese and English are fairly different after all and we just try to use English grammar as a reference for making it easier to grasp. You could think about「いつ」as "undefined-time (that is to be specified)" to make it a noun, if that helps.
I'm not really sure what kind of answer anyone can offer beyond what Fovulonkiin has already explained, and I don't know of any moderators who answer questions besides Swisidniak in some of the earlier parts of the course.
Even in English, "when" can be a pronoun:
Other times, the word “when” is classified under pronouns if it is used to represent an unknown or unspecified time. For instance, in the example:
You need the report by when?
The word “when” is considered as a pronoun because it represents the unknown time when the report is needed.
This idea of "undefined time" as a pronoun that Fovulonkiin suggested is even used in English and I think is a great answer to the question.
As Helgemonster pointed out, itsu means "when", but tada sometimes means "free", just a different meaning of "free".
In this exercise, we are learning ひま which means "free" as in "having spare time". The hints (which I agree are terribly unhelpful) ただ and 無料の (muryou no) mean "free" as in "no cost". Also, the other hint that I get, 自由な (jiyuu na) means "free", but in the sense of "unrestricted" or "liberated".
It's also worth noting that ただ also means other things like "just" and "only" in other contexts. In my experience though, when you receive something for free from a store or restaurant, サービス (saabisu) is more commonly used than ただ, possibly to avoid ambiguity from these extra meanings.
I also put 暇がいつですか and was marked wrong and ironically what you say doesn't make sense is currently the given standard answer for this question.
"When is (your) free time?" and "(Your) free time is when?" are essentially the same, right? Unless we're missing something and someone can explain why one or the other are wrong I'll just report it as possible answer.
I struggle with n desu as well. Right now I think it may be used with other question words to get the reason for something. In this same lesson the word なぜwas used and んです was used there. For example, why is it that you were late? This probably makes no sense as I am trying to figure it out too. Maybe a Japanese native or expert can help us. :)