What is the ruling on reciting the Chapter after Al-Faatihah , and what should a worshiper who forgets it do?
All perfect praise be to Allah, The Lord of The Worlds. Any other part of Qur'an that a worshiper reads after Al-Faatihah during the first and the second Rak`ahs is a Sunnah, and forgetting to do so doesn`t nullify prayer, and doesn`t require performing Sujood As-Sahw (prostration of forgetfulness). 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.
Which hour coincides with the last third of the night?
This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.
What are the Sunnahs and etiquettes recommended for the person offering the Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
There are several Sunnahs and etiquettes that are recommended for the person offering the Udhiyah (sacrifice) to observe, including:
1-It is Sunnah for the one intending to sacrifice to refrain from removing any hair or nails once the first ten days of Dhul-Hijjah begin. The Prophet (peace be upon him) said: "When the ten days [of Dhul-Hijjah] begin and one of you intends to offer a sacrifice, let him not touch [remove] any of his hair or skin." [Narrated by Muslim]. If someone does remove any hair or nails, they have not committed a sin, and their sacrifice remains valid.
2-It is recommended for the person offering the sacrifice to slaughter the animal themselves. If they are unable to do so, they should witness the slaughter. The Messenger of Allah (peace be upon him) said to Fatimah (may Allah be pleased with her): "Stand and witness your sacrifice, for indeed, with its first drop of blood, your [previous sins] are forgiven." [Narrated by Al-Bayhaqi and Al-Tabarani; it is classified as a weak (da'if) hadith].
3-The animal should be positioned to face the Qiblah at the time of slaughter, as the Qiblah is the most noble of directions.
4-The slaughterer should say: "Bismillah ar-Rahman ar-Rahim" (In the name of Allah, the Entirely Merciful, the Especially Merciful). Even if one forgets to say it, the sacrifice is still permissible to eat. Allah (Blessed and Exalted be He) says: "So eat of that [meat] upon which the name of Allah has been mentioned" [Al-An'am: 118]. It is also recommended to send blessings upon the Messenger of Allah (peace be upon him) and to say "Allahu Akbar" (Allah is the Greatest) after the Tasmiyah.
5-The slaughterer should pray for the sacrifice to be accepted by saying: "O Allah, this is from You and for You, so please accept it from me." (Allahumma hadhihi minka wa ilayka, fataqabbal minni). And Allah the Almighty knows best.
