We're looking at the potential to finish our basement out, but I'm not sure what all needs to be done with our setup first. Basically, we have a basement under half of our house, the other half is a dirt crawl space that has two little vents, one on either side. Between the two zones is a solid poured wall. The floor joists span across and so in between each is a slot between the two.
The house is old and so more recently they added/updated the HVAC. This included a new heat pump outside, furnace/air handler/fan inside and ducts ran throughout the exposed basement ceiling to new registers in the floor above. So as to add registers to the back of the house, above the crawl space section, they busted out a rectangular hole into the wall between the crawl space and basement and ran a duct branch that way. I've included an ms paint floor plan and side view to get an idea of what I mean.
(Blue lines in basement section are windows, orange in crawl space are vents)
My question is, what needs to be done to finish and insulate this space? Should the crawl space be sealed off completely from the basement section? Including the hole surrounding that main duct and the gaps between the floor joists above?
Although there are downwards facing registers in the basement ceiling as well, I leave them shut off because it would seem pointless to try and heat/cool the space if it just flows out the crawlspace?