Bic answered the first half of your question. I don’t know what lens you are coming at this from, so I’ll dump a little bit of medical and biochem in the answer.

As for the second half, if turnover rate goes down, neurotransmitter duration of action is increased. One such drug class that has that action are cholinesterase inhibitors (-stigmines). Their action increases the synaptic half life of acetylcholine by inhibiting acetylcholinesterase, and that manifests as increased cholinergic activity (SLUDGEM or DUMBBELLS are two menonics you can look up if you’d like). Stigmines are reversible and competitive (until they aren’t…they eventually can “mature” into irreversible) so they only impact Vmax, not Km.

Anti-cholinergics do the opposite action at those synapses. They bind the ACh receptor without producing an effect increasing accessibility of ACh to acetylcholinesterase. I can’t comment to what degree this effect increases the turnover of ACh. The Km of acetylcholinesterase from a quick google is somewhere in the realm of 10 mM making me think it does not operate in a saturated fashion, but it’s been a decade since I’ve learned this stuff. It seems increasing substrate supply would increase rate too.

Hope this helps.