Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?

Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.

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 offer prayer at home, or should it be offered in the mosque?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                                      It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.

Do certain vaginal discharges and incontinence of urine nullify ablution, and should underwear be changed?

A person afflicted with constant impurity due to urinary incontinence and vaginal discharges is obliged to make ablution for every obligatory prayer when its time is due, and after removing Najaasah (impurity), and wearing a clean diaper. He/she is obliged to pray immediately even if the impurity is being released, and he/she is obliged to remake ablution, and the aforementioned for every obligatory prayer.