looks and sounds like MG to me, seen it a lot with folks birds. Would take testing to confirm, your local NPIP agent can do it for you. Basically a respritory infection. Eye swelling , head shaking, sneezing, snotty discharge all signs of it.
Time and anitbiotics for CRD (Chronic Respritory Disease) are the best route if this is what it is. They shouldnt die from it like that though. Runny faomy yellow poop mentioned is often signs of worms or internal parasites too.
Try worming them good first, wazine is a poor wormer only gets 1 kind. Use Safegard 3 cc per gallon or ivermectin (as injectable or por on though, it's not water soulable, 1/2 -1 1/2 cc per bird, depends on size)
Brown, tarry, super smell poop is a sign of coccidia, very common in all young birds. Older ones tend to fight it off better. Even on medicated feed, birds can still get it as the dose in feed is not always accurate. Use any sulfur based meds for it in their water. Corid is a very common product for it.
Then again, could be one of any of a lot of other things, but these are the 3 most common problems from the symptoms given and pic shown. All put together, yes, they would feel awful, stop eating, and eventually die
