Why don't you buy longer complete lengths and trim them down to suit your ceiling height, it will surely look more seamless than multiple lengths butted up against each other, which are likely to not align very well unless you have dead straight walls/corners.
Can a 'corner bracket' (whatever that is) be justified by your SE? Surely to get a splice plate to work you would need to be able to push it into the (presumably non existent gap) between the top of the joists and the underside of the deck?
As mentioned can just some of them be sistered rather than every one and why do the sister joists need to be as deep as the main joists? So you can still have a soffit, albeit with a deeper fascia.
If they want justification then justification you will have to provide. They are excessive, they look to be much smaller than the fascia (or perhaps the photos are deceiving?) in which case why are they notched so much? I would hazard remedial work could include sistering say every third joist...
Haha, it was a tongue in cheek offer really, it's probably completely knackered/rotten still having been sat inside it's box in the garage for the last couple of decades! :p
Probably condensation in this situation, the nail is a cold bridge from the rafters (which are coldish) to the inside head of the nail (which are warm) so condensation forms around them. Nothing else you can do other than improving the insulation situation, I wouldn't worry and it's not a big worry.
I used to have a pull down screen fixed to the wall, worked a treat, a black border makes a big difference IMO. Still got it in the garage actually, god knows why, you can have it if you can collect it. :p