1. If an adult man says to an adult woman in private that he accepts her as his wife and both of them say alhamdulillah, will they be married as per Islamic law? If yes, then is it mandatory to divorce this women before the same man marries another women?

2. What is the ruling of divorce if the woman is pregnant? Is it permissible for a husband to divorce his wife during pregnancy?

1. No marriage took place. So no divorce is necessary after fornication or adultery.

2. It is permissible to divorce a woman during pregnancy however the iddah does not end until the delivery of the child.