Any son of Poseidon and a mortal woman is a demigod, as Polyphemus, Orion and Theseus. They did not belong to the sea.
God of the sea - yes.
Demigod of the sea - no.
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No. She was a daughter of Phorcys and Ceto, both of whom were a minor god/goddess of the sea.
Demigod of the sea. He is the son of Poseidon. His upper body was human and his lower half was sea creature-like
Achilles was the demigod of war.
Given that his mother was Aethra, who most recount as mortal, and he was fathered by both Poseidon the sea god and Aegeus, yes.
No, Hades is not a demigod. He is a full God, and a very powerful one at that.