Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Should one obey his mother even if she was wrong?
Obeying one`s mother is an obligation in matters that are beneficial to her and so long as she didn't drive her children to commit an act of sin.
Is it permissible to divide the Aqeeqah amongst one`s brothers and family?
Giving a portion of the Aqeeqah, even a small one, to the poor and needy is obligatory, and if one`s brothers and family are among the needy then, they are more entitled to it, and this way it is a charity and an observation of kinship ties. However, if they aren`t needy then, it is permissible to give them from the Aqeeqah after giving the poor and needy their share.
I married a man and had two children; however, we got separated four years ago. In addition, my husband`s brother, paternal uncle of my children, has been providing for them ever since. In fact, he is an honest, well-behaved man. Is it permissible that we get married although his brother (My ex-husband) is still alive?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is temporarily prohibited for a woman to marry her stepbrother. Therefore, once she receives Talaq Ba`in (Irrevocable divorce), she is allowed to marry her stepbrother, even if his brother (First husband) is still alive. And Allah The Almighty Knows Best.