Appointment of directors as per ca 2013

1. Yes additional director can sign the balance sheet as he will be director having all rights of a director on date of signing of balance sheet. But be sure, the additional director need to be regularised on date of agm only.

2. Secondly, at every general meeting at least 2 members in person need to be there for quorum purpose, in case of private limited companies. so no doubt NRI can appoint a proxy in his place but presence of at least 2 members is must. so better is to transfer some shraes in name of additional directo so that in case NRI is not present, the additional director after being the shares transferred can be the part of quorum.

3. One more thing is that as stated by you that NRI director will not be present in any meeting of director in an year will disqualify him to be the director of the company. Under CA 2013, a director need to attend atleast one board meeting and if he does not, he needs tio vacate his office as director of the company.