an eyeabolt is a piece of rigging hardware wiht a ------ which means it has a series of spiral grooves cut into it.

Answer 1

Thread

(threaded like a bolt, which is what it is with an eye cast or forged at the head.)

Answer 2

Beware of eyebolts if loaded in tension (pulling out from the attachment) because then the whole load is taken by the thread. They are much safer if loaded mostly in shear.