Statement 1 is correct. Article 361(2) of the Constitution of India provides that no criminal proceedings whatsoever shall be instituted or continued against the President, or the Governor of a State, in any court during his term of office. Statement 2 is correct. Article 158(4) states that the emoluments and allowances of the Governor shall not be diminished during his term of office. This provision ensures the financial security and independence of the office of the Governor.