Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
What is the ruling on omitting the prostration of recitation?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The prostration of recitation (Sajdat al-Tilawah) is a Sunnah for both the reader and the listener. There is no sin in omitting it, though doing so results in missing a great reward. Muslim narrated from Abu Hurairah (may Allah be pleased with him) that the Prophet ﷺ said: 'When the son of Adam recites a verse of prostration and prostrates, Shaytan withdraws weeping, saying: "Woe to him! (and in the narration of Abu Kuraib: "Woe to me!") The son of Adam was commanded to prostrate and he prostrated, so Paradise is his; and I was commanded to prostrate and I refused, so the Fire is mine."'
Sheikh al-Islam Imam al-Nawawi (may Allah have mercy on him) stated: 'It is recommended to prostrate immediately after reciting or hearing a verse of prostration. If one delays it but the interval is short, he may still prostrate. However, if the interval is long, the opportunity is missed.' [Rawdat al-Talibin Vol.1/P.323].
Furthermore, the prostration of recitation becomes obligatory (Wajib) in congregational prayer if the Imam prostrates, out of the necessity of following him. And Allah the Exalted knows best.
What is incumbent upon the one offering the sacrifice if, after slaughtering the animal, they discover that one of its internal organs is damaged or diseased?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The presence of disease or defect in the internal organs of a sheep does not affect the validity of the sacrificial animal, unless the disease leads to the animal becoming emaciated and its meat becoming corrupted.
It is stated in al-Iqnā' (2/590) by Imam al-Shirbīnī: "The third disqualifying condition: an animal with a manifest illness — meaning one whose illness visibly results in emaciation and corruption of its meat. However, if the illness is minor and does not produce such effects, it doesn`t affect the validity of the sacrificed animal." And Allah Almighty knows best.
Is it permissible to offer an Udhiyah on behalf of the deceased?
In the Name of Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Offering an Udhiyah (sacrificial animal) on behalf of a deceased person is permissible. This is the official position of the Hanbali school (as stated in Kashshaf al-Qina’ by al-Bahuti,Vol.6/P.428) and was also upheld by the prominent Shafi'i scholar Al-’Abbadi (mentioned in Bidayat al-Muhtaj by Ibn Qadi Shuhbah,Vol. 4/P.358). It has likewise been narrated as a valid view among some Maliki and Hanafi scholars.
In fact, Imam Abu Dawud dedicated an entire chapter in his Sunan collection entitled, "Chapter on Sacrificing on Behalf of the Deceased." In it, he recorded a narration from Hanash, who said: "I saw 'Ali sacrificing two rams, so I asked him, 'What is this?' He replied, 'The Messenger of Allah (peace and blessings be upon him) commanded me to offer a sacrifice on his behalf, so I am sacrificing on his behalf.'"
Imam Abu Dawud also narrated from Jabir (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "O Allah, this is from You, for You, and on behalf of Muhammad and his Ummah (community). In the Name of Allah, and Allah is the Greatest," and he then slaughtered the animal.
The textual evidence here lies in the fact that our Master, the Prophet (peace and blessings be upon him), offered a sacrifice on behalf of his entire community—and it is well-established that his community includes those who have already passed away.
Furthermore, there is an abundance of sacred texts demonstrating that the rewards of righteous deeds reach the deceased. For instance, it is permissible to fast on behalf of a deceased person who passed away with missed obligatory fasts, and it is equally permissible to perform Hajj on their behalf, both of which are firmly established in authentic Hadiths. Therefore, if the reward of fasting (which is a purely physical act of worship) and Hajj (which is a joint physical and financial act of worship) can reach the deceased, then the reward of an Udhiyah reaches them with greater reason (by way of A Fortiori argument). This is because it is a purely financial act of worship, falling under the general category of charity (Sadaqah).
Additionally, scholars have reached a consensus (Ijma') that the rewards of charity reach the deceased, and since the Udhiyah is inherently an act of charity, it falls under the same ruling. Consequently, based on all the aforementioned evidence, we hold the view that offering a sacrifice on behalf of the deceased is entirely permissible. And Allah the Almighty Knows Best.