It sounds like your birds could have Infectious Laryangotracheitis (sorry if I didn't spell that right), which is a viral respiratory disease of birds. It is characterized by coughing (sometimes coughing up bloody mucus), swollen sinuses, watery eyes, choking, gasping, sneezing, lethargy, and in severe cases, death. Unfortunately, there is no treatment for Laryangotracheitis; affected birds may recover, but many will die. I am very sorry if I am correct in my diagnosis.
It is possible that I am wrong, though I can't think of any other respiratory disease that causes bloody nasal discharge and such sudden death. If you want, you could purchase Tylan50 or Tylan200, which are both strong antibiotics used in treating respiratory diseases. You can usually find Tylan at a livestock supply store. It comes in an injectable form, and in a powdered water soluble form. The injectable form works faster, but if the powdered form is the only one available, it will work, too.
The Tylan50 injectable dosage is 1cc for large-fowl, .5ccs for bantams, injected into one side of the breast once daily for 5 days. The Tylan200 injectable dosage is .5ccs for large-fowl, .1-.3ccs for bantams, injected into one side of the breast once daily for 3-4 days. When injecting Tylan, alternate the side of the breast that you inject into, and use a small gauge needle, as Tylan can make the injection area sore. Depending on the age of your chickens (they look young in the photos), I would adjust the recommended dosages slightly because they are meant for mature chickens.
I don't know the powdered Tylan50 or 200 dosage, as I've never used it, but if you search around on the Backyard Chickens website, you should be able to find it. During Tylan treatment, do not give probiotics, dairy products, or Apple Cider Vinegar. Vitamins/electrolytes are fine, though. If the Tylan is effective, results are usually seen after 2-3 days of treatment.
Once again, I am sorry that you are having this trouble with your birds.
The best way to prevent diseases like Laryangotracheitis is to vaccinate your chickens.
