"I am not going to go to the school."
Translation:Δεν πρόκειται να πάω στο σχολείο.
The sentence is vague. I would use the sentence "I am not going to go to school tomorrow." and provide as translation "Δεν πρόκειται να πάω στο σχολείο αύριο." Even without any modification, I would remove the other "correct" answer "Δεν πρόκειται να πηγαίνω στο σχολείο." The later corresponds to "I will not be going to school." and demonstrates a continuity of action.
Πρόκειται has two meanings 1) is about to happen, may happen 2)concerns, is a matter of sth. Πρόκειται να πάω διακοπές σύντομα=I am about going (going to go) on vacation soon. Δεν πρόκειται για ανθρώπινο λάθος=It's not a matter of human mistake. Either way, this chapter will change in the new tree, there is no need for a chapter only for πρόκειται
It is colloquial, but very commonly used. In fact, it's much more common to hear this phrase without στο.
There are also other phrases with similar structure, like πάω σπίτι, πάω γυμναστήριο, πάω φροντιστήριο, πάω μπαλέτο... My personal guess it that, when going somewhere becomes a habit, people tend to talk about it in a more general way. Therefore they omit the article.