What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?
All perfect praise be to Allah, The Lord of The Worlds. Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.
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.