On the issue of each member having its own government, and of how rights and restrictions transfer across the Federation, in TNG it was shown that applicants for Federation membership were assessed for suitability, which involved determining whether the society was mature enough.
Perhaps part of that assessment was to make sure that the laws the applicant imposed on its own beings would be sensibly adapted to the alien worlds of the other members, in order to render the question of incompatible rights a non-issue.
Part of maturity is getting along well with others.