Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
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.
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
I`m keeping a plot of land (10 Dunums) for my children. Is it liable for Zakah?
Praise be to Allah, The Lord of the Worlds.
Land that is purchased with the intention of ownership and personal benefit—meaning to retain it for use and not for trade—is not subject to zakāh, as such property is not considered from trade commodities (ʿurūḍ al-tijārah).
It is stated in Al-Ḥāwī al-Kabīr:
“If it is property and one intends it for trade, then zakāh is due upon it; but if he intends it for personal possession, then no zakāh is due upon it.” And Allah, the Exalted, knows best.