According to the provisions of Article 32 of the Marriage Law, if one spouse has an affair and the other spouse files a divorce lawsuit, if mediation fails, the court shall grant the divorce. So, your divorce request can be realized.
2. About compensation.
According to the provisions of Article 46 of the Marriage Law, you, as the innocent party, have the right to claim damages, including compensation for mental damages and compensation for material property losses. There is no quantifiable fixed standard for compensation for mental damage, and the law only provides six reference contents, which are generally decided by the court after comprehensive consideration. Judging from judicial practice, it will not exceed 50 thousand yuan, usually several thousand yuan. In this case, the amount you can ask the other party for compensation shall not exceed 20,000 yuan. Compensation for material losses requires you to prove the amount of the loss. So you need to provide all the expenses during the wedding.
3. About crime.
As for the "how to sue them" you mentioned, legally speaking, I can't help you. There is no "adultery crime" in modern China, so the man who has sex with the woman cannot be investigated for legal responsibility. As for the woman's legal responsibility, you can't pursue her criminal responsibility except civil responsibility. There is no crime of "cheating on marriage" in law, only the crime of bigamy, but the woman's various behaviors only belong to cohabitation and do not constitute bigamy.
4. About mutual punishment.
If you really want to punish the woman, you can consider telling the truth to the public through the media, so that everyone can see the true face of the woman. But judging from the social effect, you will inevitably be implicated, even you are more affected than that woman. Special reminder, be sure to state the facts truthfully, otherwise, you may have to bear legal responsibility.
5. About protecting yourself.
No matter how you handle this matter, from a legal point of view, I suggest you: collect and keep the evidence. Including: marriage expense documents, evidence of the other party's affair and so on.