What is the meaning of the Udhiyah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The Udhiyah (Sacrificial Offering) refers to the livestock (An'am) that is slaughtered as an act of drawing closer to Allah the Almighty. This takes place on the day of Eid al-Adha (the 10th of Dhu al-Hijjah) and during the three days of Tashreeq that follow the day of Eid. And Allah the Exalted knows best.
How is the beginning of Ramadan determined?
1. Completing 30 days of Sha‘ban, or
2. Sighting the crescent moon after sunset on the 29th day of Sha‘ban.
It is Sunnah to search for the moon, and it is obligatory to follow the official authorities responsible for announcing it.
What is the ruling on one who doubts washing a limb before or after finishing ablution?
If a person performing ablution doubts leaving the washing of a limb from the limbs of ablution during his ablution, he must repeat washing that limb and wash what comes after it. If he doubts leaving the washing of a limb after finishing the ablution, there is nothing upon him. And Allah the Almighty knows best.
Is "Bismillāhir-Raḥmānir-Raḥīm" a verse (āyah) of Sūrat al-Fātiḥah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The basmalah ("Bismillāhir-Raḥmānir-Raḥīm") is, without question, a verse (āyah) of the Noble Qur'an, and according to the Shāfi‘ī school, it constitutes a verse of Sūrat al-Fātiḥah itself. Al-Fātiḥah is a pillar of the prayer, and it consists of seven verses, of which the basmalah is one. The prayer is not valid without reciting it, nor if any of the Fātiḥah's verses, letters, or shaddahs (consonant doublings) are omitted or altered.
It is stated in Bushrā al-Karīm (Vol.1/p.202), from the books of the Shāfi‘ī school: "The basmalah is a complete verse of it [i.e., of al-Fātiḥah] in practice — and it suffices, for this to be established, that there be strong probability (ẓann), especially given that this has come very close to certainty (yaqīn), due to the consensus (ijmā‘) of the Companions on its inclusion in the muṣ-ḥaf [the written text of the Qur'an] in its script, despite their extreme diligence in excluding from it anything that did not genuinely belong to it — to the point that they even [carefully regulated] its diacritical dots and vowel markings." And Allah, the Exalted, knows best.