Nikaah & Marriage Issues

Nikaah in the state of janaabat

Q: I had zina with a girl (both of us are unmarried) right 1 hour before our Nikah, we didnt got time to take a bath and we completed our nikah like that only. Is my nikah valid or invalid? Should I have to do again nikah with her?

Important Note: The girl had zina with a person long time ago in her teenage years, in her past...and she repents it. After that I had married her. 

Invalid nikaah

Q:

1. A man says to a woman,’Did You marry Rahim?’ The woman replies,’Yes’ in front of many people. Does it mean they are married?

2. A man says to a woman, ’Are you marrying Rahim?’ The woman replies,’Yes’ in front of many people. Are Rahim and the woman married?