Explanation:

- Statement 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 is correct as per Article 361 of the Indian Constitution, which provides immunity to the Governor from being answerable to any court for actions performed in the exercise of official duties.

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

- Correct according to the same Article 361, protecting the Governor from criminal proceedings during their tenure.

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

- True, as per Article 194, providing legislative privileges and immunity to the members for speeches made and votes given in the legislature.

Answer: Option 4: I, II and III