Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible for a financially capable woman to pay the Zakat to her sons or one of them?
It is permissible for a mother to give her children from zakat if they are eligible to receive it, even though she is obligated to provide for them. This is based on the saying of the Prophet Muhammad (PBUH) regarding Zainab, the wife of Abdullah Ibn Mas'ud (may Allah be pleased with them): "Your husband and your children are more deserving of your charity" [Al-Bukhari]. And Allah Knows Best.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
My husband wanted to sell a piece of land that was his own, but his father insisted that he transfer the land in his (the father’s) name so that he could sell it at a higher price. Then, my husband and his father would split the price. After my father-in-law sold the land, he denied everything and refused to acknowledge my husband’s right. My father-in-law passed away a year ago, and my husband’s brothers divided the inheritance, refusing to acknowledge that this land was a trust held by their father for my husband until it was sold. Are they sinful for knowingly denying that the land belongs to my husband, and what is the ruling on praying against them?
All perfect praise be to Alalh, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
Among the rights of the deceased upon their heirs are: preparing them for burial at death, settling their debts, returning people’s rights to them, executing their will, and then dividing their estate. What was mentioned in the question falls under the rights of others, even if they are among the heirs, and the deceased is not absolved of it unless it is returned to its rightful owners. This is because Allah, Almighty, forbids consuming others' wealth/properties unjustly. However, do not give up on seeking a solution by involving righteous and well - respected individuals who may have influence over them, in the hope that Allah guides them to goodness and correctness. As for supplicating against them, the prayer of the oppressed is not rejected, even if the oppressed person is not a Muslim. And Allah knows best.