director of company

yes, he can be director in another company also.

Yes he may venture into the same business, however, in respect to that company he would be considered as Related Party and in both companies he has to submit his interest and any transaction or agreement with both of the Comapnies will be under the purview of Related party Transactions under section 188 of the Companies Act, 2013.

Yes as per Section 165 of the Companies Act 2013, a person can be a director in maximum 20 Companies out of which 10 shall be the public Company and the Director shall give the disclosure of such Directors in Form MBP 1 as per Section 184 of the Companies act 2013