I had 'I will not go to the school' for which I was marked wrong. I don't know why this alternative but correct form of the future was not accepted, nor why the 'the' before 'school' was not either. If one isn't going to school as a pupil on a regular basis, one might be going to the building anyway, in which case 'the' is appropriate. In any case, 'going to school' does not always imply futurity but continuous activity.
Strangely enough, it was not included. All our versions were "I am not going to go to school." Basically "Δεν πρόκειται να... means "I am not going to..." and would normally require another verb but in this case, it is accepted as is.
In my view: "I am not going to go..." is closer to the meaning since it shows more determination but it's a very thin line.
I definitely understand the structure at play here with (δεν) πρόκειται να but I guess it is just the fact that both the auxiliary verb and the main verb in this phrase is "go" so "going to go" can often be substituted for just "going to" in English at least...if it were any other verb, it would not be possible (e.g. "I am not going to cook" is not necessarily the same as "I am not cooking" although it can convey the same idea in certain contexts.)
From what I understand, πρόκειται is more literally "about (to)" or "will/want (to)" (that is why one must use να after it), so I don't think you can say πρόκειται στο σχολείο... without including the να plus the main verb. If you did, it would be like saying "I'm about/will school" which obviously is ungrammatical. Interestingly, in other languages this is actually possible (e.g. German "Ich will nach Griechenland."= "I want (to go) to Greece".) I hope that helps. Note: I am not a native speaker of Greek- wait for someone else to confirm what I have written.