first wife

Q: A girl wants to marry me and I want to marry her too. But we had physical relation About 2 years ago. In these two years i got married with other girl and now we also had a kid. But the first girl who had physical relation with me is still want too marry me. And i am thinking(planing) to make her my 2nd wife. She is agree and my wife is also agree with it too. What should i do. Is there any way(kaffara) to get married(2nd).

Q:

1. Is there a difference in nikaah and marriage?

2. Is it permissible to have a nikaah with someone else even when you are married?

3. Is it compulsory to have permission from wife and children (all well grown up) to have nikaah with someone else (due to total / negative and un acceptable cooperation in life from wife)?