Both statements are correct as they reflect the constitutional protections afforded to the Governor of a State under Article 361 and Article 200 of the Indian Constitution. Article 361 provides immunity from criminal proceedings during the Governor's tenure, ensuring that the Governor can perform their duties without the fear of legal repercussions. Article 200 guarantees that the emoluments and allowances of the Governor cannot be diminished during their term, which is vital for maintaining the independence and integrity of the office. These provisions underscore the essential balance between accountability and the functional autonomy of constitutional authorities in India, which is a key concept in understanding governance in a federal structure.