Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?
The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.
Is it obligatory to have the intention for each day of fasting, or is one intention sufficient for the whole month?
The intention is obligatory for each day of Ramadan because each day is an independent act of worship separate from the others.
The intention must be made at night before the break of dawn, as the Prophetﷺ said: "Whoever does not intend fasting at night, there is no fast for him." [An-Nasa’i]
And he also said: "Whoever does not firmly resolve to fast before dawn, there is no fast for him." [At-Tirmidhi, Abu Dawood, and An-Nasa’i]
Whoever wakes up and eats Suhoor while mindful of fasting has made the intention. Likewise, one who firmly intends at any moment during the night to fast the next day has also fulfilled the intention.
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 to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.