क्या तुम परसों स्कूल जाओगे? तुम परसों स्कूल जाओगे? परसों स्कूल जाओगे?
These are all ways of asking the same yes/no question. In the first one, the word क्या "warns" you that a question is coming up. In the second one, by the end of the sentence (either seeing the ? mark or hearing the intonation) you realize it is a question. In the third, we don't know it is being directed at "you" until we see the conjugation for the "tum" form of the verb, at the end.
Yes, the function of क्या as a yes/no question word was made clear earlier in the course. Over time in this lesson, it has become clear to me that this is simply the तुम form of the future tense. Without any sort of Tips & Notes, though, I feel quite in the dark when new verb forms are introduced. Some Indo-European languages (maybe only the Celtic ones) have separate forms of the verb only to be used in forming questions, so I was wondering whether this ending might be that. Clearly, it isn't.
I suppose they want you to acknowledge the future tense of the verb, as opposed to using the present progressive tense and adding a future time ("day after tomorrow") and just implying future action. The goal here (I assume) is to learn the actual future tense. Moreover, in Hindi, for what it's worth, there's a certain definiteness about the actual future tense (WILL do) as opposed to the the less definite "planned action" in your sentence.