If I used the instrumental of a song and the hook but wrote new lyrics for the verse using a completely different cadence what terminology would I use in the song title?
Traditionally, in American pop music, the core of the song is considered to be the vocals/lyrics. Therefore if you keep the vocals and change the instrumental, it's a remix. New lyrics and vocals over an existing instrumental would be considered a derivative song, or possibly a brand new song sampling the old song (although you wouldn't typically use the entire instrumental in that case). Finally, a cover has the original lyrics and roughly the same melody, but new vocals and instrumental (it's a karaoke cover if you use the original instrumental). In any of these cases, if you make money off the song, the original songwriters are considered your cowriters, and are entitled to a share of your profits, even if you don't keep anything they explicitly contributed. (Freestyle has two meanings, neither of which apply here. The older, obsolete meaning, is a rap with no focused subject or theme. The contemporary meaning is an improvised rap created simultaneously with being performed.)
It's a term of art, however, and not a scientific classification, so there are ambiguities. For instance, you're keeping the original hook --if the hook is the real core of the song, then you might call your version a remix. Or, if some of the original verses are still in the song, it might be considered a remix.
Interestingly enough, in Jamaican dancehall music, the relationship is reversed. The riddim (instrumental) is considered the core of the song, and the vocals are interchangeable.
You may find it interesting, that the re-use of the same melody for a different text was already done by classical composers. The technical term at that time was parody, in the meaning, that different lyrics were used. This was done extensively by J. S. Bach when he reused melodies from secular cantatas for religious ones or vice versa, as well as by Handel, when re-using the music from an aria in a new opera (where the text of course needed to be completely replaced), sometimes combined with a musical overhaul as well.