Custody of children

Q: My husband and I are seperated and he sent a letter that states that if I sign this than only divorce will go throught.i als have a 2 year old girl.

1. In that letter it states that once a month on weekend he is allowd to take my daughter and from fri to Sunday. My daughter is too small and doesn't leave my side. islamically is this allowed?

2. Do I have to pay half of my childs needs including education food etc?

3. In the list of what was mine in the house its not complete and there is no mention of the mehr. Is he allowed to keep the mehr?

Q: In the case of divorce, a four month old girl from the wife's previous marriage was looked after and brought up by step father for many years. So who does gain the custody of the girl?

Q: If the children are being deprived of visiting the father by the mother, what should be done?

Q: In the case of divorce if the wife does not remarry any one and stays single, who does the children go to? Under the custody of the mother or the father?

Q: After both parents death, who becomes the legal guardians of the kids in Islam especially considering issues of mahram in a daughters case.

Q: What should a husband do/fulfil in all perspectives of life for kids/wife after separation or divorce?

Q: Whom does islam gives the first right to the child if the parents have a fight, the mother or the father? If the mother is ill does that gives a vaild reason for the father to keep the child?

Q: Whom does Islam give the right of the child after the parents. The mother's family or the father's family.

Q: In the case of divorce, which parent has the right of custody of the children and up to what age? If a certain parent has the right of custody then can that parent prevent the other parent from visiting the children? Similarly, I would like to know which parent has to provide maintenance for the children. If the children have wealth, can their wealth be used for the maintenance? What exactly does maintenance entail and will the expenses of the children's education also fall under maintenance?  

Q: My mother is divorced due to 30 years of abuse. My father abuses me and my sisters as well. She is remarried now. My sisters wants to live with my mother as our father hurts us and breaks our souls down and our minds. Is it permissible for us to live with my mother as her husband is a very good man Alhamdulilah?