Dear Mr. Anand, all proposals will have some conditions so your feeling that there is a catch is ok.
The society has to follow the nomination form name/(s) without any hesitation. The nomination system has been created to avoid unnecessary issues for the society as well as the society member. As I have said earlier, the nominees do not become owners but they have to distribute the ownership as per the shares of the legal heirs.
The society cannot initiate the proceedings suo moto ie. on their own but on the application by a person who has interest in the issue such as yourself or any one of the nominees, the society can put the names of the nominees.
You are right about your share from your father adding to your earlier 50% but to confirm I may have to see your earlier ownership details and the nomination forms.
Anyone who is in occupation of the flat can either stay or rent it out. They may be legal or illegal occupants and their action could also be legal or illegal. If anyone feels it is illegal and is a concerned party say yourself, you may send a notice to the party to desist from doing so. If the party disagrees, then you will have to go through the legal process by taking help of a legal expert.
But do remember that it is better to resolve differences within the family as it is ok to lose something to your near and dear ones than to fight and lose money for the legal process.
S Jadhav