Tom, yes, I think that open area should be closed. It may have been left open originally with plans of a second flu or combustion intake for your fireplace. Just be sure to keep any insulation, etc. clear of the metal firestop and flu area.
I suspect that your insurance will cet this up as a claim, especially if this may have been ongoing. It's likely that the roof decking on that side of the home is damaged. Probably not visible damage at this point, but if it's been getting wet like that you may be able to see slight sagging between rafters from the outside.
It sounds like you're on the right road to repair now, Tom. I wish you all the best for a happy ending.