Good thing I was a contractor
You are talking a WHOLE lot of stuff in that little post…
Firstly, you need to talk to a code person. Every city, county, brothers sisters uncle Fred, has rules about exposure, fire rating etc. The rules for exposed ceiling are for prep areas and what not but not for seating areas.
If the insulation is loose (hung between the rafters by staples, tie wire or string, or with insulation hangers) you can’t expose the ceiling without encapsulating it in sheeting of some kind. That is completely related to what code issues you have to deal with locally.
Some codes allow for the original stuff to come out and a spray foam application to be installed, painted and what not but that is still an ugly exposure for an open ceiling.
FYI… when a building is built that is spec’d for an exposed ceiling they do the insulation ON the roof surface, above the rafters topped off by the roofing, and usually rock top surfacing. You are probably going to find it difficult to get the exposed rafter look without actually having the mentioned roofing installed which is VERY expensive.
Just a construction primer
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