maybe
Many things. Hawks, Owls, Kestrels, other birds of prey. Cats, snakes.There are many more. Anything that's a predator AND has the ability to move fast or hover in the air, will probably eat birds.
Any bird of prey that includes birds in it's diet will likely eat the head too. It provides food, and so it is eaten.
Yes. In some cases. For example the Sparrowhawk and other birds of prey eat smaller birds such as..... sparrows.
It is because their mouths are thin, can eat worms.