Directors

(1) does the director who comes at vacancy of non rotaional director u/s 262, vacate office in next agm or hold office till the unexpired term of that previous director? (2) if original director is non rotational, should alternate director u/s 313, hold office beyond agm if original director has not returned in the state of board meeting? (3) If board has delegated powers to another director or committee. Can such director/committee pass a resolution without board meeting or quorum?