Issuing talaaq in exchange of the money agreed upon

Q: My question is regarding khula. The wife demanded for separation from her husband and husband was not ready. Finally he agreed for separation (divorce) with a condition of their son's custody and return of mahr and other financial settlement. The entire process was done in India by a lawyer on a legal paper and husband pronounced talaaq three times at one go (please note he had issued one talaq already few years ago) and they got separated. Now my question is, is this considered as second talaaq or khula? Also please be informed that they lived together 2 months after this procedure. So if this is khula that took place, is it right on them to live together? Are they sinning? Request you to kindly respond at the earliest so that I can stop them from sinning further or help them in the best possible way pleasing Allah.

Not living with the new husband out of fear of losing custody of one's children

Q: I have a Muslim co-worker that got married a few months. She was a divorcee. The man she married has a teenage son from a previous marriage. She herself has 2 pre-teens. One being a girl. She does not live with this man as she's scared her ex-husband (whose been married for over 6 yrs now) will gain custody of the children. How valid is that marriage? The new husband is building a house so that her daughter can have her own room and bathroom in the house. By the time the house is built the girl will be 12 and the new husband's son will be 14. Is that allowed in Islam?