"I come home at half past two."
Translation:मैं ढाई बजे घर आता हूँ।
I'm not a native speaker, but बजे here is an adverb; so it doesn't decline, it's not a plural of 'बजा' (which is an inflection of the verb). For it to be a verb here you'd have to rephrase it to be something like 'I come home when it is [hitting] half past two': '... बज रहा है'।
It might be fine colloquially (or not, I don't know) - but generally the subject comes first, so, as in the given answer, 'मैं डाई बजे...' - ordered like a 'subordinate clause' in English: 'I, at half-past two, come home'.
Same as the way we've seen हर दिन used in other lessons' sentences.