The correct answer is option 3: Both 1 and 2.

Statement 1 states that no criminal proceedings can be initiated against the Governor of a state during his term of office. This is in accordance with Article 361 of the Constitution of India, which grants the Governor of a state immunity from criminal proceedings during his term of office. However, it is important to note that this immunity does not extend to civil proceedings against the Governor.

Statement 2 states that the emoluments and allowances of the Governor of a state cannot be reduced during his term of office. This is in accordance with Article 158 of the Constitution of India, which states that the emoluments and allowances of the Governor shall not be diminished during his term of office. This provision ensures that the Governor is not subjected to any financial pressure or influence that may affect his decision-making.

It is important to note that the immunity and protection granted to the Governor of a state is not absolute. If the Governor commits any criminal act or violates any law, he can be impeached by the State Legislature on grounds of violation of the Constitution or gross misconduct. Similarly, the emoluments and allowances of the Governor can be reduced if he is found guilty of any misconduct or violation of the law.

In conclusion, both statements 1 and 2 are correct, as they are in accordance with the relevant provisions of the Constitution of India. However, it is important to note that the immunity and protection granted to the Governor is not absolute and is subject to certain limitations and conditions.