Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
What is the ruling on someone who possesses cash reaching the niṣāb (minimum threshold liable for zakah), and then uses part of it to purchase gold before the ḥawl (lunar year) is complete — must he pay zakāh on all of it [combined], or only on the remaining cash, excluding the gold?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Gold acquired for hoarding and saving is subject to zakāh once it reaches the niṣāb (minimum threshold liable for Zakah) — when combined with any cash held — and once a full ḥawl (lunar year) has elapsed over it. The starting point for calculating this ḥawl is the ḥawl of the paper currency [used to purchase it], which had already reached the niṣāb and was then used to purchase the gold.
It is stated in Mughnī al-Muḥtāj (Vol.2/p.78): "As for someone who sells silver in exchange for gold, or vice versa, zakāh remains obligatory upon it, since he builds [the calculation of] its ḥawl upon [the ḥawl established at the time of] the original transaction [i.e., when the wealth was first acquired]."
This has already been explained in detail in Fatwa No.
2670 — please refer to it.
And Allah, the Exalted, knows best.
Is it permissible for a woman to wear underwear while performing Umrah?
Yes, it is permissible for a woman to wear underwear while performing Umrah. This is because she should keep her regular clothes that cover all her body while being in a state of Ihram (ritual consecration) for Hajj, or Umrah. However, she should uncover her face and hands, but it is permissible for her to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.