I want to know what anyone with a fair amount of knowledge about birds of prey thinks of a owl/hawk that sings while perched before hunting.?
You could imagine that your fictional bird of prey emits various sounds to mimic the animals it intends to prey upon and therefore draw them out. Like human hunters who use different techniques or specially made lures (sound makers) to imitate the calls of animals like ducks or deer to attract or confuse them. You could go further and create a fictional hawk/owl hybrid that is able to shape-shift into forms that resemble its chosen prey animals, or it can transform into shapes that its prey animals visualise as deities or spiritual figures. In Watership Down, Richard Adams creates the character Lord Frith, who is analgous with the Sun, and who the rabbits regard as their God and as the figure who comes to collect them upon their death. A predator who appears as the Sun immediately before death would serve to blind victims, as well as giving them a reassuring sense that they have been called to their maker (which as they are about to be killed and eaten, they in fact have been). This in turn could serve as a myth among prey animals that if they look directly at or see the Sun, they will die. However, because their enemies/predators can appear as the Sun, the prey animals will find themselves looking into it despite trying not to - which reinforces the myth among the prey animals that the myth is true.
The First Dragon
Birds of prey don't let out a war cry before hunting, any more than a human hunter lets out a cry before hunting. If you are hunting for food, or hunting to kill for any reason, you will be as silent as possible. They don't want to warn their prey. On the other hand, if they are attacking a rival of the same species, they will make noise. They will hope that the rival will retreat or surrender without a fight. You will see this even in your yard, when two birds argue [chirp at each other] until one of them flies away. If this fails, they may fight, but rarely to the death. Neither humans nor other animals usually want to kill members of their own species, if they can avoid it. I have seen birds' response when a raptor appears, even silently; they hide immediately, and they stop singing too. When there is a raptor in the neighborhood, often the prey birds even cease to sing for territory. No doubt they still challenge each other in more subtle ways; but they are careful not to draw the raptor's attention. So, letting out a "war cry" before hunting for food is totally out of character. You don't go to war with your food source. You just go out and get some with as little fuss as possible.
It would be ridiculous to give a bird of prey a sound that indicates it is about to hunt. Immediately its prey is put on notice that it is about to hunt. It would then have a somewhat difficult time finding prey. However, if you are writing fantasy fiction I do not know why you seek zoological facts. You can have anything do what you want in such writing.