Does an internal examination require ghusl?
Ghusl isn't required for making internal examination; however, it invalidates one's fasting. And Allah Knows Best.
How should I be kind to my atheist father?
Allah, The Exalted, has decreed and ordained his slaves to be kind with parents, even if they are polytheists, by honoring and obeying them in all that isn`t sinful, so that they might love Islam and embrace it as a result.
Is it permissible for a father to disinherit his disobedient, alcohol consuming son and his daughter who had fled home and never returned?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is permissible to give heirs some money because of their being extra obedient or needy. As far as inheritance is concerned, it is to be divided after one`s death, so it had better be left to the court itself. And Allah The Almighty 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.