You are within your rights by most state laws to shoot the neighbor's dog if it molests your livestock. I've had this problem with a couple of my neighbors, and I felt no reluctance in laying down the law to them - confine your dogs or they will be shot and you will be notified to come pick up the dead bodies. I meant it. These people knew I meant it. The dogs were confined or given away. Problem solved.
Your property is for your use, not your neighbor's dogs' use, and your livestock most certainly doesn't exist for the pleasure and entertainment of the neighbors' dogs. A little assertiveness can make life so much better for everyone. Neighbors sometimes need training just as their animals do. The law is on your side. Remember that.
Your chickens would do much better kept separate from the ducks. Chickens thrive much better in flocks consisting of just chickens. Hens need exercise and sunlight to be able to absorb vitamin D and this is necessary to absorb calcium. Improper absorption of calcium results in reproductive issues, often leading to death. Poor calcium absorption can lead to egg binding due to poor shell quality, shell-less eggs, and even unregulated ovulation. Hens need lots of room to range and exercise outdoors in direct sunlight for best quality of life.
Your run is only just barely adequate for that many chickens. If you were able to get the neighbor to confine their dog, the hawks would be manageable by putting up low ramada-like structures for them to run under if they spot a hawk overhead. Dogs are your worst predator, but you can shoot them, while the hawks are protected.
