What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah 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.
What are the Sunnah acts of fasting?
● Delaying Suhoor (pre-dawn meal) as long as there is no risk of Fajr beginning.
● Hastening Iftar (breaking the fast) immediately after confirming sunset.
● Performing I‘tikaf, especially during the last ten nights of Ramadan.
● Reciting the Quran frequently.
● Avoiding idle and useless talk.
● Being generous and charitable.
● Guarding oneself from desires.
● Purifying oneself from major impurity (janabah) before Fajr.