What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. And Allah Knows Best.
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. 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.
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.