What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.
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.
What is the ruling on fasting?
Fasting in Ramadan is an individual obligation (Fard ‘Ayn) upon every mature, sane Muslim who is capable of fasting.
Fasting can also be recommended (Mustahabb), such as voluntary fasting on Mondays and Thursdays, fasting on the Day of Arafah for those not performing Hajj, and fasting on Ashura.
Fasting can be prohibited (Haram), such as fasting on the two Eid days, the Day of Doubt (Yawm al-Shakk), and the Days of Tashreeq.
Some types of fasting are disliked (Makruh), such as singling out Friday or Saturday for fasting without a specific reason and fasting on the Day of Arafah for a pilgrim.
What is the ruling on reciting the takbīr from Sūrat aḍ-Ḍuḥā to Sūrat an-Nās upon completing the recitation of the Qur'an (khatm)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is recommended to recite the takbīr from the beginning of Sūrat aḍ-Ḍuḥā through to the end of Sūrat an-Nās, and this is the recitation practice of the people of Makkah.
It is stated in Nihāyat az-Zayn (p. 65): "It is sunnah to begin each sūrah with the basmalah, since it constitutes a verse of it. It is also sunnah to say, before each sūrah — from aḍ-Ḍuḥā to the end of the Qur'an — 'Lā ilāha illallāh, wallāhu akbar' (There is no god but Allah, and Allah is the Greatest), based on what has been narrated regarding Imam ash-Shāfi‘ī (raḍiyallāhu ‘anh), who heard a man reciting this takbīr in prayer, and said to him: 'You have done well, and you have hit upon the sunnah.'"
And Allah, the Exalted, knows best.