In general we only see the operations of a small part of starfleet, not the federation itself, so we don't really know how it is meant to function. It could function like the EU, where centrally decided edicts filter right down to the laws of the land in a rather petty manner, or be more like the UN (which is what I have always assumed the federation to be modelled on) where internal issues are not tightly constrained, beyond a few issues of basic law such as 'humanoid rights', a non-aggression pact (enforced by the absorbsion of a world's military into starfleet) and probably a ban on dictatorships, and decrees restricting trade of certain banned goods. A model like the EU, or even where the member worlds would be like the states of the USA would seem to contradict the non-interferance policy.
Although, given that the federation is run from Earth, likewise starfleet, the federation is in effect, a human empire, where members do seem subservient to human policy.
The federation does seem eager to admit as many newly 'ready' worlds as soon as possible, which would make it expansionist in nature. For example, although i was window dressed as an issue of taking care of a weak race, for the greater good, in the face of a tyranny, the federation's attempts to admit Bajor was probably initially about squeezing the Cardassians, instead of actually looking out for the bajorans, then with the wormhole, it became a military strategic necessity. Sussing out of places like Kesprytt and Malcor would seem to be an attempt to ensure that these worlds never become a threat to the federation by remaining independent. The prime directive, with respect to places like that seems to be more a way to duck responsibility, rather than to actually 'protect' these worlds.
So IMO Garak and Quark are right, and that the federation is tolerated (or liked) by its population seems to be to do with the way that the apparent freedoms and needs of the 'man on the street' are respected.