Nikaah & Marriage Issues

Husband not taking care of the needs and expenses of his wife and children

Q: I am a working woman and married. Both me and my husband are working in respectable jobs. I handle my own personal expenses from day one of marriage and have never asked for pocket money from my husband. 

I have two children aged 1 year and 1 month. My husband refuses to help in the my children's financial needs. Both of them are on formula milk and their combined expenditure is around 80000 which I am solely bearing along with my own expenses. 

My husband's income is more than me. He refuses to contribute even half. Alhamdulillah, I am managing but my question is what are the rights of such a husband/father over his wife and children if he refuses to contribute even 50 percent financially if he has more than enough money. What are the faraiz and instructions for the mother/wife in such a case who despite being married is living like a single mother?

Continuing a marriage if the mahr (dowry) has not been paid

Q: Is it permissible to continue a marriage if the mahr (dowry) has not been paid? 

I am currently married, but my husband has not yet paid the agreed-upon mahr (dowry). I would like to know if my marriage is still valid in Islam without the payment of mahr. What steps should be taken in such a situation? Is the marriage still considered valid, and what are the Islamic guidelines regarding mahr payments? Should I take any specific actions to address this issue?

Husband giving the false impression that he was not married when taking a second wife

Q: My husband didn't clarify about his previous marriage to me in our Nikaah certificate. He mentioned that he was divorced from his previous marriage but after our marriage he disclosed to me that his ex is still his wife and I am his second wife. 

My question is that, is our Nikaah done or because of his statement our Nikaah is not valid? Please clarify.