Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?
Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.
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 permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.