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.
This makes sense, as the Federarion has guarantees for rights for both member worlds and their populations.
Given Bajor as an example, it appears that there are options to allow a member world to voluntarily leave.
The Federation also, from what we've seen, protects free travel and trade between member worlds, and seems to have a unified currency to augment local financial systems, the Federation Credit.