(A) Correct — “Hit the nail on the head” means doing something exactly right.
(B) Correct — “Under the weather” means feeling sick.
(C) Correct — “Let the cat out of the bag” means revealing a secret.
(D) Correct — “We’ll cross that bridge when we come to it” means dealing with a problem when it arises.
Hence, all (A), (B), and (D) are correct idiomatic usages.