post-divorce

(I run an NGO) This forum is a boon to india, as it eases out a lot of complicated minds and throws light on the most controvercial issues which remains unsolved and unanswered in the court of law. so firstly thanking all the advocates writing in this forum. My query is- my friend has been seperated for 5 years and recently signed a mutual consent divorce with no alimony and very small maintainance for her 2 daughters. Her married life with her x was just for 1 yr and she has twins. Now after divorce she wants to remarry a widower man who has one son, their understanding is excellent and all 3 children are classmates and they a great family, However the daughters hate the previous father(natural father) and he has their visiting rights. and he also has taken the right to take the daughters home one weekend in a month as part of their mutual consent. Now, the the lady wants to remarry and i have following queries 1)can she keep her prev marriage name as the daughters name is the same , after her remarriage? 2)If she changes her name then can she change her daughters names as well as she has the permanent custody, but we have a strong doubt that the prev fathers NOC if required for name change he may not give 3)to change the daughters name does her new husband need to adopt them? 4)how can she and her daughetrs have the same name after her remarriage registration BIG THANKS TO ALL OF YOU