Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
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.
Does touching one's wife invalidate ablution?
Touching the wife according to the Shafi'ee's doctrine invalidate husband's ablution. And Allah Knows Best.
What is the ruling on ablution if vaginal discharge is expelled, and is it impure?
If these discharges exit from the external genitalia (apparent part of the vagina), they are not impure and do not invalidate ablution. If they exit from the internal part, they are impure and do invalidate ablution. If it is uncertain whether they are from the internal or external part, they are not impure and do not invalidate ablution.
The apparent part is what becomes visible when sitting, and what the husband's penis reaches during intercourse is considered part of the apparent. The internal part is what is beyond that. And Allah the Almighty knows best.