[subject] + 才 + 不 / 没 + [verb phrase] + 呢
[subject] + 才 + [adjective] + 呢
[noun] + 才是 + [noun]
[clause] + 才对 / 才行
In speech, 才 before the predicate can insist on something, usually against what someone else said or assumed. There is no sense of lateness, and 呢 usually closes the sentence.
With a negative, 才 rejects an idea outright. It's defiant or teasing, and it belongs to talk between people who know each other. 才没 denies something happened; 才不 refuses or denies a state.
This 才 doesn't take 了.
Said back with 你 as subject, it turns an accusation round: "you're the one who's…".
才是 corrects: not that, this. It often follows a negative clause or a mistaken guess.
Before an adjective, 才…呢 means "now that really is…", usually trumping something just said.
At the end of a clause, 才对 says "that's the right way" and 才行 says "that's what it takes".
The fixed frame 不…才怪 "it'd be a wonder if not" uses the same 才.