Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.
What is the ruling on swearing a false oath by the Holy Quran?
Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.
What is the ruling on the fasting of a woman who has reached menopause if menstrual blood flows?
If a woman reaches the age of menopause (which is usually sixty-two) and her menses have ceased, then she sees blood after that, and its duration is not less than a day and a night (24 hours), it is menstruation (hayd). If it is less than a day and a night, she is considered as having non-menstrual vaginal bleeding (mustahada), so she fasts and prays. However, she must perform ablution for every obligatory prayer after its time enters, pray immediately, and be treated as a person with a continuous condition. There is no specific end limit for a woman's menstruation; it is possible as long as the woman is alive. And Allah the Almighty knows best.
What is the Islamic ruling on smearing the head of the newborn with the blood of the `Aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (makrūh) to smear the head of the newborn with the blood of the 'aqīqah, as this is a practice that belongs to the customs of the pre-Islamic era of ignorance (Jāhiliyyah). What is Sunnah instead is to anoint the newborn's head with saffron or another pleasant fragrance. And Allah Almighty knows best.