I am not understanding if your refusal to take any step is stemming from your fear that given the strong laws in favour of women, she may later on make your life miserable or whether it is on account of any financial dependence on your wife and in-laws. However this fear is going to achieve nothing and just make you feel that there is a constant sword hanging over your head. Firstly, collect a copy of her statement and the entire investigation from the Police Station. Appoint a private PI and obtain concrete proof of her relationship. Once you have all the proof, you can file for Divorce on the ground of adultery and cruelty.
1. You can initiate complaint under Sec 497 against the man.
2. There need not be any agreement. She can live with him as long as she desires.
3. She can file for Divorce but unless she is able to mask her affair and produce incriminating evidence against you, she is not liable to succeed.
4. No live-in relationships have no time limit or completion date.
If you genuinely want to save the marriage, try reaching out to her, talk to her, go for marriage counselling.