Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.
What is the ruling on the ablution of one who washes his arms from the wrist to the elbows?
In the school of Imam al-Shafi'i (may Allah have mercy on him), washing the arms (hands) is achieved by washing the arms completely, from the fingertips to the elbows. Washing only the palms at the beginning is insufficient, as washing them at the beginning is a Sunnah, but after washing the face, it becomes obligatory (fard). The person performing ablution must wash his palms along with the arms after washing the face. If he does not wash his palms, his ablution is invalid and not correct. And Allah the Almighty knows best.
What is the wisdom behind legislating the Udhiyah?
The Muslim must know that through the Uḍḥiyah, he complies with the command of Allah, the Exalted, and performs a worship that brings him closer to Allah and distances him from the Fire.
The Uḍḥiyah holds profound wisdoms and noble meanings, including:
1-Reviving the Sunnah of Abraham, peace be upon him: He complied with Allah's command when He ordered him to slaughter his son Ishmael. Abraham, peace be upon him, succeeded in the test, and when he was about to slaughter his son, Allah sent down a ram to ransom Ishmael and commanded him to slaughter it instead. Allah, the Exalted, says {what means]: "And when he reached with him [the age of] exertion, he said, 'O my son, indeed I have seen in a dream that I [must] sacrifice you, so see what you think.' He said, 'O my father, do as you are commanded. You will find me, if Allah wills, of the steadfast.' And when they had both submitted and he put him down upon his forehead, We called to him, 'O Abraham, You have fulfilled the vision.' Indeed, We thus reward the doers of good. Indeed, this was the clear trial. And We ransomed him with a great sacrifice." [Al-Ṣāffāt/102-107]. Thus, the sacrificial offering became an enduring Sunnah until the Day of Judgment, and Muslims offer their wealth as sacrifices, drawing closer to Allah, the Exalted, reviving this great Sunnah.
2-Providing abundance for people on Eid day and the Days of Tashrīq: Among the wisdoms of the Uḍḥiyah is that the Muslim provides generously for his family, neighbors, relatives, and the poor during these days. The Muslim is encouraged to eat from his sacrifice, give charity from it to the poor, and gift from it to his wealthy neighbors. Thus, goodness spreads throughout the entire community. The Prophet, peace and blessings be upon him, said: "The Days of Tashrīq are days of eating and drinking." (Narrated by Muslim). Allah, the Exalted, says {what means}: "And the camels and cattle We have appointed for you as among the symbols of Allah; for you therein is good." [Al-Ḥajj/36]. This good includes the good of both this world and the Hereafter.
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.