Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the ruling if hemorrhoid blood exits after completing ablution?
If this blood is exiting from outside the anus (due to the hemorrhoid protruding), it does not invalidate ablution, because blood exiting from the body from other than the two orifices does not invalidate ablution. If it exits from the anus (meaning from inside it), it invalidates ablution, and one must perform istinja' from it, wash the area of impurity, and repeat the ablution.
However, if this blood exits continuously such that no time remains sufficient for purification and prayer without it flowing, then it takes the ruling of urinary incontinence (sals al-bawl). One then cleanses from it after the time for each prayer enters, performs ablution immediately thereafter, and performs the obligatory prayer immediately. There is no liability upon him after that if something of it flows, and he may pray as many voluntary prayers as he wishes. If he wants to pray another obligatory prayer, he must cleanse himself and perform ablution. And Allah the Almighty knows best.
What is the ruling of Islamic Law on a father shaking hands with his son’s wife after she has been divorced three times?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The wife of one’s son is among the women permanently prohibited to the husband’s father as soon as the marriage contract is concluded, based on the saying of Allah the Exalted: “Prohibited to you are your mothers, your daughters, your sisters, your paternal aunts, your maternal aunts, your brother’s daughters, your sister’s daughters, your foster mothers, your foster sisters, your wives’ mothers, and your stepdaughters under your guardianship [born] of your wives with whom you have consummated marriage. But if you have not consummated marriage with them, there is no sin upon you. [Also prohibited are] the wives of your sons who are from your loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful.” [al-Nisāʾ/23]
This prohibition begins once the son’s marriage contract with his wife is complete, and it remains in force even if the son separates from her before consummation or before any seclusion (khalwah) with her. It is therefore permissible for the father to shake her hand and to be alone with her, provided there is no fitnah (temptation) and no suspicion.
It is stated in ʿUmdat al-Sālik (p. 204): “It is forbidden to marry… the wives of one’s fathers and of one’s sons. All of these women become prohibited by the mere contract, … all of that being a permanent prohibition.” End quote, with slight adaptation. And Allah Almighty knows best.
What is incumbent upon the one offering the sacrifice if, after slaughtering the animal, they discover that one of its internal organs is damaged or diseased?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The presence of disease or defect in the internal organs of a sheep does not affect the validity of the sacrificial animal, unless the disease leads to the animal becoming emaciated and its meat becoming corrupted.
It is stated in al-Iqnā' (2/590) by Imam al-Shirbīnī: "The third disqualifying condition: an animal with a manifest illness — meaning one whose illness visibly results in emaciation and corruption of its meat. However, if the illness is minor and does not produce such effects, it doesn`t affect the validity of the sacrificed animal." And Allah Almighty knows best.