The way his conviction wavers as he says it also shows that he's trying to convince himself and justify his actions to himself more than anything else. It's not that he can live with it, it's that he has to live with it.
They're actually a republic. The Vedek Assembly has a lot of influence, but they're fully separate from the Provisional Government. And they only have that much influence because the vast majority of the population follows the Bajoran faith. Think of the Assembly like the Vatican - powerful when everyone cares (Pope during the Middle Ages), but virtually powerless when nobody does (Pope now).
and they certainly treated specific items as “valuable” (historical items, weapons, and especially liquor.)
Historical items definitely have non-monetary value. They can't truly be replaced since, no matter how accurate the replica, only the one chair will be the Enterprise-A's captain's chair, for example. Replicators have software restrictions on what you can make with them, so you can't just replicate weapons under normal circumstances, which creates scarcity and gives them value. Starfleet replicators also seem to be restricted from creating alcohol, which means most of the characters we see can only get it on shore leave, which also creates scarcity and therefor value. Alcohol is probably significantly less scarce when sourced through civilian replicators. The ones on DS9 are programmed with Starfleet's restrictions, though.
Common misconception. There were several different emblems for different parts of the fleet, but each ship did not have a unique emblem. Someone from the costume department assumed that each ship had a unique emblem and one episode had it wrong, but we also have the memo telling them to not do that again.
I dunno, having Yar's baby momma show up and drop off a kid would have been a challenge to write in the late 80s / early 90s.