Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
How should I deal with the whispers of the devil with regard to ablution and purity?
Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.
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.