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.
Is it incumbent on a family to provide for its old handicapped son and take care of him?
The family and relatives - e.g. brothers - of such a person are obliged to spend on him and take care of him if he didn`t have money of his own.
Is it permissible for a person who hasn`t made ablution to call for prayer (Adhan)?
All perfect praise be to Allah, The Lord of The Worlds. It is disliked for a person with a minor impurity to call for prayer, but if he does , then it`s valid and sufficient. And Allah Knows Best.
Is it allowed for a Muslim woman to wear nail polish?
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.
Nail polish is an adornment that a woman is allowed to wear for her husband, and not in the presence of non-Mahram men. However, during ablution water needs to reach the nails, so it isn`t possible to perform 'Wudu (ablution) with nail polish on. Therefore, it isn`t valid to make Ghusl Jnabah (Ghusl performed after sexual intercourse or ejaculation), Ghusl after menstruation and Ghusl after Nifas (blood of childbirth) while wearing nail polish. And Allah The Almighty Knows Best.