as per regulation 31(1) clauses xii and xiii read with regulation 42(ii) clauses e and f, of the DCPR 2034, a chajja is exempt from computation of FSI
However i do think that the BMC's permission for carrying out any work would be required, even though BMC may not grant separate approval for constructing a chajja (particularly since the chajja do not reflect in the sanctioned building plans). So a construction permission including a commencement certificate from BMC would be required under the applicable provisions of MMC Act, 1888 and MRTP Act, 1967
as regards your 4th query, a proper resolution needs to be passed by the society considering majority votes of members who are present and entitled to vote at a special meeting of the society held for the purpose
please also consult an architect for this