In ayyuhā al-nāṭiq, ayyu is the vocative noun, hā a particle drawing attention, and al-nāṭiq its identifying description. Al-muballigh adds a further description of the same person.
Hal ordinarily introduces a question. Here it conveys reproach or rhetorical objection: when will the allegations stop? In li-dhāka intihāʾun, the prepositional phrase may serve as an advanced predicate and intihāʾun as the delayed subject.