The decapitated head hanging by his own hair is from "The Servants of Bit-Yakin" (frequently anthologized under the alternative title "Jewels of Gwahlur"):
He approached the lotus grove by a circuitous movement, and scarcely the rustle of a leaf proclaimed his passing. At the edge of the trees he halted suddenly, crouched like a suspicious panther among the deep shrubs. Ahead of him, among the dense leaves, showed a pallid oval, dim in the uncertain light. It might have been one of the great white blossoms which shone thickly among the branches. But Conan knew that it was a man's face. And it was turned toward him. He shrank quickly deeper into the shadows. Had Zargheba seen him? The man was looking directly toward him. Seconds passed. The dim face had not moved. Conan could make out the dark tuft below that was the short black beard.
And suddenly Conan was aware of something unnatural. Zargheba, he knew, was not a tall man. Standing erect, his head would scarcely top the Cimmerian's shoulders; yet that face was on a level with Conan's own. Was the man standing on something? Conan bent and peered toward the ground below the spot where the face showed, but his vision was blocked by undergrowth and the thick boles of the trees. But he saw something else, and he stiffened. Through a slot in the underbrush he glimpsed the stem of the tree under which, apparently, Zargheba was standing. The face was directly in line with that tree. He should have seen below that face, not the tree-trunk, but Zargheba's body—but there was no body there.
Suddenly tenser than a tiger who stalks his prey, Conan glided deeper into the thicket, and a moment later drew aside a leafy branch and glared at the face that had not moved. Nor would it ever move again, of its own volition. He looked on Zargheba's severed head, suspended from the branch of the tree by its own long black hair.