Short answers, pulled from the story.
Hyperion was one of the Titans in Greek mythology, the father of Helios, Selene, and Eos by his sister-wife Theia. The name Hyperion also belongs to a son of King Priam of Troy and served as a secondary name for the sun god Helios.
Hyperion's children were Helios, Selene, and Eos, born of his union with his sister Theia.
Hyperion translates from ancient Greek as 'the high one,' written in Greek letters as Ὑπερίων.
Hyperion's wife was Theia, who was also his sister. The ancient sources describe her as his sister-wife.
Yes, a prince of Troy named Hyperion was one of the sons of King Priam. His mother was never identified in the ancient sources, recorded only as an unknown woman.
Hyperion served as a byname for Helios, the sun god, meaning it functioned as a secondary name that could stand in for Helios directly.