Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
My mother inherited a share from my late father`s and brother`s property; however, the inheritance, a piece of land, wasn`t divided amongst the eligible heirs because it was hard to sell. While alive, she used say that she wanted these shares to be distributed amongst the poor and needy. What is the ruling of Sharia on this?
All perfect praise be to Allah, the Lord of the worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
This is a will, so we have to consider the estate she had left behind. If the piece of land, which she had willed, equals one third and less of her estate, then the will must be executed. But, if it is more than one third, then one third must be executed and the rest of the estate, if the heirs agreed, is to be executed as part of her will as well. However, if the heirs haven`t approved of that, then what remains, excluding that one third, must be divided amongst them according to the Islamic rules of inheritance. Moreover, we recommend that you pay a visit to the Iftaa` Department to make things clearer for you. And Allah The Almighty Knows Best.
Is it permissible for the mother to offer an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)for her son?
Aqeeqah is due on the one obliged to provide for the newborn, and it is permissible for the grandfather, or the mother to offer the Aqeeqah.
Is it permissible to pay the expiation of an oath to a charitable party as it feeds the poor and needy such as Tkiyet Um Ali?
There is no harm on authorizing someone to handle the expiation of another to the poor and needy, since Shafiee's jurists stated that authorizing someone for the purpose of distributing Zakah, expiation and vow is permissible as stated in [Mughni Al-Muhtajj,vol.3/pp.237]. At last, the intention of the person who intends to authorize someone else suffices in this regard. And Allah Knows Best.