Is "He is not necessary" a correct translation?
No - that would be Δεν είναι απαραίτητος with masculine ending.
Oh, logical, thanks.
'It is not needed' is marked as wrong. The same meaning in English.
It is unnecessary?
It's certainly not what the sentence says, but is there a word for "unnecessary" besides saying this?
There are a couple: https://www.wordreference.com/engr/unnecessary.