Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
What does (Whoever fasts Ramadan with faith and seeking reward) mean?
This phrase is part of a hadith in which the Prophet ﷺ said:
"Whoever fasts Ramadan with faith and seeks his reward from Allah, their past sins will be forgiven." [Agreed upon]
The meaning is:
● They fast Ramadan with firm belief that Allah has made it obligatory.
● They fast out of obedience to Allah, knowing they will meet Him.
● They hope for reward from Allah and fast purely out of their faith while seeking His reward.
What is the Islamic punishment for the one who neglects prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Neglecting the prayer (Salah) is among the major sins (Al-Kaba’ir). One who neglects it out of laziness is considered a transgresor (Fasiq), while one who neglects it while denying its obligation is a disbeliever (Kafir). And Allah the Exalted knows best.
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.