Is it permissible for a person who has to make up for missed fasts to fast six days of Shawwal (the month directly after Ramadan) before making up for the missed fasts?
Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.
What is the ruling on reciting verses of the Holy Quran on water, then drinking it?
It is permissible to recite Quran on water, then drink it as a kind of treatment since the Quran heals. Allah, The Almighty, Says (What means): "We send down (stage by stage) in the Qur’an that which is a healing and a mercy to those who believe: to the unjust it causes nothing but loss after loss." [Al-Isra`/82].
Is it permissible for the big brother to force his sisters to wear Hijjab (Islamic wear) if their father didn`t do his part in this regard ?
All Perfect Praise is due to Allah, The Lord of The Worlds
The father`s attention should be drawn gently and politely, and the sisters should also be reminded with good words since Allah, The Almighty, Says (What means): "O ye who believe! Save yourselves and your families from a Fire whose fuel is Men and Stones." [Al-Tahreem/6]. And Allah Knows Best.
A sixteen-year-old young woman suffers from Alopecia, and lost her hair and eyebrows as a result. Is it allowed to draw her eyebrows using henna and an eyeliner?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for women to use henna and what the asker has mentioned isn`t considered hair extension. However, if this young woman is proposed to, she must disclose this matter to the person proposing to her to avoid deception. And Allah The Almighty Knows Best.