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).
Does the fast become invalid if water from rinsing the mouth reaches the stomach while performing ablution?
If water reaches the stomach without the fasting person exceeding normal rinsing or being excessive, their fast remains valid.
However, if they exceed the normal practice or exaggerate in rinsing, causing water to enter the stomach, their fast is invalid.
This is because excessiveness in rinsing is prohibited for a fasting person, as the Prophetﷺ said: "Exaggerate inhaling water during ablution, except when you are fasting." [Narrated by the Four Imams]
Transgression (Ta‘addi) refers to rinsing the mouth more than three times, while exaggeration (Mubalaghah) includes gargling, drawing water deep into the nasal passages, or filling the mouth with water in an unusual manner.
Does swallowing a fly, road dust, or flour dust break the fast?
A fasting person does not break their fast if something enters their body cavity against their will, such as a fly, road dust, or flour dust.
What is the ruling on istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.