What is the wisdom behind the legislation of fasting?
Fasting is a divine school from which the believer learns much and trains in virtues that may be needed in life. Among these virtues is patience, as it is the month of patience. Fasting also teaches honesty and consciousness of Allah in both private and public, for there is no observer over the fasting person in abstaining from lawful pleasures except Allah alone.
Fasting strengthens willpower, sharpens determination, and nurtures mercy and compassion among the servants of Allah. It is a struggle against the self, a restraint of desires, a purification of the soul, and a cultivation of goodness.
The Prophetﷺ said: "Allah, the Almighty, said: ‘Every deed of the son of Adam is for him, except for fasting; it is for Me, and I shall reward for it. Fasting is a shield. So when one of you is fasting on a day, let him not engage in obscene speech or raise his voice in anger. If someone insults him or fights him, let him say: I am a fasting person. By Him in whose hand is the soul of Muhammad, the breath of the fasting person is more pleasant to Allah than the fragrance of musk.’" [Bukhari and Muslim]
Is it permissible for a woman to uncover her face while performing Umrah (minor Hajj)?
The woman while in a state of Ihram (ritual consecration) is obligated to uncover her face and hands, but at the same time permitted to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
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.