Insulation, furring/framing, and drywall has considerable weight. It needs to be accounted for.
That "cross-beam support" is a rafter tie; it isn't intended to carry any vertical loading (really shouldn't have a punching bag hanging from it).
If you only intend to heat/cool the building part time (didn't answer that question), I'd be concerned about indoor humidity.
I'd spend some time analyzing span charts, with a mind toward the rafter loading (don't forget snow load!) before deciding the dead load capacity. While the span...
No idea where you are in the world, but Tractor Supply carries Crown PSC 1000 (basically a Stoddard solvent) for a reasonable price. You will need to run a pump with solvent-tolerant seals.