My suspicions are you have a very hungry snake that's eating eggs and trying to eat your chickens. One way to find out is to stop gathering the eggs. If the snake gets its belly full it'll stop killing your chickens.
The birds all show signs of being suffocated or poor circulation(heart attack) which makes me lean towards it being a snake after chicks or eggs. 3 of the deaths could possibly be due to the roosters trying to defend the chicks, broody hens and pullets.
Snakes also leave little to no signs of...