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 combining (jam‘) and shortening (qaṣr) prayers when travel is repeated on a daily basis?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
A traveler is permitted to avail himself of the concessions of shortening and combining prayers once the distance of his journey reaches (81 km) or more. This is on condition that his journey is a permissible one, and that he begins shortening and combining only after setting out and passing beyond the built-up limits of the city in which he resides, or beyond the administrative boundaries of the area where he lives.
Accordingly, if the distance between one's workplace and one's place of residence reaches the distance upon which the concession of combining and shortening depends, then combining and shortening are permissible once he leaves the built-up area, even if this travel is repeated on a daily basis.
Ash-Shirbīnī (raḥimahullāh) said: "It is permissible to combine Ẓuhr and ‘Aṣr, either as an early combination (taqdīm) in the time of the first, or as a delayed combination (ta'khīr) in the time of the second; and likewise Maghrib and ‘Ishā' — either early, in the time of the first, or delayed, in the time of the second — during a long, permissible journey, in following [the Prophet's practice]. As for the delayed combination, it is established in the two Ṣaḥīḥs from the ḥadīth of Anas and Ibn ‘Umar (raḍiyallāhu ‘anhum). As for the early combination, Ibn Ḥibbān and al-Bayhaqī graded it ṣaḥīḥ from the ḥadīth of Mu‘ādh, and at-Tirmidhī graded it ḥasan." [Quoted with slight abridgment from Mughnī al-Muḥtāj, Vol.1/p.529]
The conditions for combining and shortening have already been explained in Fatwa No. 14 and Fatwa No. 842. And Allah, the Exalted, knows best.
Must a person refrain from eating for the rest of the day if they break a fast of a vow (nadhr) or a make up fast (qada)?
Whoever observes a vowed fast (nadhr) or a makeup fast (qada) is prohibited from breaking it without a valid excuse. If they break it without a legitimate reason, they are sinful.
However, they are not required to refrain from eating for the rest of the day, because such restraint is only required out of respect for the month of Ramadan, not for other types of fasting.
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.