Explanation : 

I. The Governor of a State is not answerable to any court for the exercise and performance of the powers and duties of his/her office.

• This statement is correct.
• Article 361(1) of the Indian Constitution explicitly states that the President or the Governor of a State “shall not be answerable to any court for the exercise and performance of the powers and duties of his office or for any act done or purporting to be done by him in the exercise and performance of those powers and duties.”

II. No criminal proceedings shall be instituted or continued against the Governor during his/her term of office.

• This statement is correct.
• Article 361(2) of the Indian Constitution 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.”

III. Members of a State Legislature are not liable to any proceedings in any court in respect of anything said within the House.

• This statement is correct.
• Article 194(2) of the Indian Constitution states that “No member of the Legislature of a State shall be liable to any proceedings in any court in respect of anything said or any vote given by him in the Legislature or any committee thereof.”

Conclusion: All three statements are correct.

Final answer: (d) I, II and III