Nikaah & Marriage Issues

Wali of a girl whose father does not want to be present for the nikaah

Q: I was divorced 20 years back and I have 2 daughters from my first marriage. My parents brought them up without any help from my ex husband.

After divorce, he got married and I also got married. Now my first daughter is getting married. For some time my ex husband is contact with my daughters so she asked her father to be her wali in her marriage but he refused all of sudden.

My father, their maternal grandfather (nana) became her wali from the age of 2 since he only taking care of her.

My question is whether my daughter's marriage is valid or not?

Marrying one's step sister

Q: My mother married a man aand they have a baby girl. After her husband died, my mother married my father then I was born.

Can I marry my half sister whose father is different and our mother is the same? We are both in love. If not, then what do we do?

Living away from one's husband

Q: I am married to a man whose hometown is 200km away from mine. He was working abroad so he promised me not to separate me from my parents before our marriage. Now he came back to our country and started a business. He stays at his home. But I still stay with my parents as they are old and sick. I am their only daughter. They don't want to let me go to my husband. I am a teacher so, I go to my husband's house only on Saturdays and Sundays. We are married for 3 years and don't have children yet. Is it good to stay away from my husband as I need to look after my parents? Is it permissible? 

Getting married to a girl who was molested in childhood

Q: A relative was investigating a girl for my marriage. He learnt from a very reliable source that the girl was sexually molested when she was a child. When my parents learnt that the girl was molested as a child, they said that we should not investigate her anymore for my marriage.

Is this correct behavior? Is this a valid reason for not considering someone for marriage? In my opinion, it appears unfair to her as she was a na-baligh at the time. I do understand well that child sexual abuse victims often carry traumatic memories and emotional symptoms well into adulthood. But will this mean that one should not consider such a person for marriage entirely before looking at anything else, like character, morality, hayaa, etc.?