You are right. बजे is the oblique case form of बजा. Sentences like "वो डेढ़ बजे जाएगा" have an implicit postposition after बजे- 'वो डेढ़ बजे (को) जाएगा'. So, डेढ़ बजा is in the oblique case in this sentence and becomes डेढ़ बजे.
I'm not sure I follow. Why does डेढ़ बजा है require the oblique case? Doesn't it translate fairly literally to "It is half past one"? Where's the implicit postposition in a sentence as simple as डेढ़ बजा है?
डेढ़ बजा है is not in the oblique case (which is why it uses बजा and not बजे). ZellieZazou wanted to know why it is बजे in other sentences like "he goes to school at half past one". I meant to say that it's because बजे is in the oblique case in those sentences.
My experience with other courses is that numerals generally are accepted, at least when giving answers in English. This course is an exception, and I disagree with their decision. Numerals are a part of language, not something different.