What should I do after learning that my wife unintentionally did not complete her waiting period ('iddah)? And must I divorce her and wait for her waiting period to end, then marry her again with a new contract? And is the first contract void?

If a woman marries while she is in her iddah (waiting period) from a previous husband, then your marriage is void, and you must separate from her immediately. She is not your wife.

She must complete the iddah of the first husband, and then observe an iddah from you.

After the expiration of both iddahs, you may marry her.

It is impermissible for a woman observing iddah to marry, by consensus, and her marriage is void.

If you separate from her, or if a separation occurs between you, she must complete the iddah of the first [husband], then observe an iddah from you. The two iddahs do not overlap because they are from two different men.