Bulugh al-Maram

Lexical Explanation:
«إِنَّا» With a kasrah on the hamzah and shaddah on the nun, it is a particle of emphasis, and in it, the pronoun is for the first person (speaker).
«أَهْلِ كِتَابٍ» "People of the Book"—these words are used for Jews and Christians. Here, in the question, Christians are mentioned. These words here are an attribute of «قَوْمٍ».
«أَفَنَأْكُلُ فِي آنِيَتِهِمْ» A doubt and hesitation would arise because the Jews and Christians would sometimes cook pork in their pots and drink wine from them, as is explicitly mentioned in the narration of Abu Dawud and Musnad Ahmad: "We used to live among the People of the Book, and we would see them cooking pork in their pots and drinking wine from their vessels." So the Prophet (sallallahu alayhi wa sallam) said: "Then do not eat or drink from their vessels." [سنن أبى داود، الأطعمة، باب فى استعمال آنية أهل الكتاب، حديث : 3839، ومسند أحمد : 193/4]
The Prophet’s answer indicates that one should avoid eating and drinking from their vessels unless there is a state of necessity. Then, when one is compelled and there is no other option left, even in that case, one should not rely on their purification, but rather purify them oneself. The prohibition in this hadith is not for the sake of prohibition (haram), but due to natural aversion, as a sound nature (fitrah) refuses to eat from such vessels and is repulsed by them, and is also repulsed by the idea of using vessels in which such filthy and impure things have been cooked.

Benefits and Issues:
➊ From this hadith, it is understood that eating and drinking from the vessels used by the People of the Book, i.e., Jews and Christians, and performing ablution (wudu) with water from those vessels, etc., is not permissible. The reason is clear: these people cook impure and filthy things in those vessels.
➋ When it is not permissible to eat and drink from the vessels of the People of the Book, then one should also avoid eating and drinking from the vessels of Hindus, atheists, and heretics in which impure and filthy things are cooked and eaten.

Narrator of the Hadith:
SR Sayyiduna Abu Tha'labah al-Khushani radi Allahu anhu: ER «الخُشَني» "Kha" with a dammah and "shin" with a fathah; he is called Khushani due to his attribution to Khushain ibn Namar (who belonged to the tribe of Quda'ah). He was among those who pledged allegiance at Ridwan. He was sent to his people, and they all accepted Islam. He resided in the region of al-Sham and passed away there in 75 AH. He was praying when his soul departed in the state of prostration. There is considerable disagreement regarding his and his father's names. He is more commonly known by his kunyah.

Hadith Commentary:
(1)
Hazrat Adi bin Hatim radi Allahu anhu belonged to a wealthy family and was prosperous, whereas Hazrat Abu Tha’labah al-Khushani radi Allahu anhu was a poor and destitute person. Both of these companions sought information from the Messenger of Allah sallallahu alayhi wa sallam regarding hunting. The Prophet sallallahu alayhi wa sallam not only granted them permission to hunt but also provided them with appropriate guidance concerning hunting.

(2)
From this, it is understood that if a person’s means of livelihood is not hunting, but he hunts as a form of recreation, as Hazrat Adi bin Hatim radi Allahu anhu used to do, then such an act is permissible and allowed. If someone’s means of livelihood is hunting and he has no other way to make a living, then he is also permitted to engage in this activity, as is evident from this hadith regarding Hazrat Abu Tha’labah radi Allahu anhu. In any case, to be excessively occupied with hunting merely as a pastime is extremely blameworthy. And Allah knows best.

Hadith Commentary:
From this last sentence, it is understood that eating carrion is not permissible.

Explanation:
By the vessels of the People of the Book are meant those utensils in which they would cook the meat of animals forbidden (haram) to eat, and those vessels in which they would drink wine. Therefore, their use was prohibited, and in cases of dire necessity, permission was granted to use them after thoroughly cleaning them.
(Fath al-Bari)

Hadith Commentary:
(1)
There is no mention of the vessels of the Magians (Majus) in this hadith.
It appears that, according to Imam Bukhari rahimahullah, the Magians are also considered among the People of the Book (Ahl al-Kitab), therefore, their vessels should also not be used.
If there is a need to use them, then they should be thoroughly washed before use.
Or, the relevance to the chapter heading is in this way: the Magians also do not avoid impurity (najasah), therefore, the ruling regarding the vessels of the People of the Book and the Magians is the same.
(2)
Hafiz Ibn Hajar rahimahullah states:
Imam Bukhari rahimahullah, through this chapter heading, has alluded to some chains of transmission (turuk) of the hadith in which the Magians are explicitly mentioned. Thus, in one narration, it is reported that the Messenger of Allah sallallahu alayhi wa sallam was asked about the vessels of the Magians, so he said:
"Wash their vessels and use them."
(Jami‘ al-Tirmidhi, al-Siyar, Hadith: 1560)
In addition, it is also the habit of Imam Bukhari rahimahullah to establish a chapter heading and then establish its ruling by way of analogy (ilhaq).
And Allah knows best. (Fath al-Bari: 9/770)

Hadith Commentary:
If an unschooled dog brings any game to you, on the condition that the game is found alive by you and you yourself perform the slaughter, then it is lawful (halal) for you; otherwise, it is not lawful. And if it becomes necessary to use the utensils of non-Muslims for food, then it is essential to wash and thoroughly purify those utensils; only then can their use be permissible for Muslims. Otherwise, it is not permissible to use their utensils.

Hadith Commentary:
(1)
In one narration, it is mentioned that Abu Tha’labah radi Allahu anhu submitted:
O Messenger of Allah! We live in the neighborhood of the People of the Book; they cook pork in their pots and drink wine in their vessels. So the Messenger of Allah sallallahu alayhi wa sallam said:
“If you do not find vessels other than theirs, then wash them thoroughly with water and use them.” (Sunan Abi Dawud, Al-At’imah, Hadith: 3839)
Regarding hunting with a sharp object, the Messenger of Allah sallallahu alayhi wa sallam said:
“When you shoot an arrow, recite ‘Bismillah’ (in the name of Allah), then if you find the animal dead, you may eat it. But if you find it fallen in water, do not eat it, for you do not know whether the water killed it or your arrow killed it.” (Sahih Muslim, Al-Sayd wal-Dhaba’ih, Hadith: 4982 (1929))

(2)
From this it is understood that one should recite ‘Bismillah’ when shooting an arrow; if the arrow is shot without reciting ‘Bismillah’, then if the animal is found alive, it should be slaughtered with ‘Bismillah’ recited. Otherwise, eating it is not permissible.
And Allah knows best.

Explanation:
1:
Whether their use and cooking or eating in them is permissible or not.

«ولحم خنزير»

The flesh of swine (is impure).

➊ As Allah, the Exalted, has said:

«قُل لَّا أَجِدُ فِي مَا أُوحِيَ إِلَيَّ مُحَرَّمًا عَلَىٰ طَاعِمٍ يَطْعَمُهُ إِلَّا أَن يَكُونَ مَيْتَةً أَوْ دَمًا مَّسْفُوحًا أَوْ لَحْمَ خِنزِيرٍ فَإِنَّهُ رِجْسٌ» [6-الأنعام:145]

➋ The jurists have reached consensus (ijma‘) on the impurity (najasah) of swine, regardless of whether it has been slaughtered or not. [بداية المجتهد 73/1] 1

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1 [بداية المجتهد 73/1، اللباب 55/1 المغني 55/1، الشرح الصغير 49/1، كشاف القناع 213/1، القوانين الفقهية ص/34، مراقي الفلاح ص / 25]

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This chapter concerns the game hunted by a trained and an untrained dog, that is, what is the ruling of the Shari‘ah regarding eating such game? The game hunted by an untrained dog is neither absolutely forbidden nor absolutely permissible; rather, there is detail in this matter: if the game hunted by such a dog is found alive and it is slaughtered (dhabiha), then it is permissible to eat it. But if the game is found dead, even if the dog has not eaten anything from it, then it is forbidden to eat it, even if the name of Allah was mentioned at the time of releasing the dog.

Benefits and Issues:
➊ The People of the Book (Christians) slaughter without mentioning Allah’s name, which is considered the same as carrion. And any vessel in which carrion meat is cooked is also impure. It is prohibited to use such a vessel without washing it.

➋ The slaughtered animals of those Jewish and Christian sects who do not slaughter without mentioning Allah’s name are lawful (halal).

➌ In our country, some Christians, when they wish to eat meat, buy it from a Muslim butcher or have it slaughtered by a Muslim. The vessels of such a Christian, whose habit is known to be this, are pure. Food cooked in them is lawful (halal).

➍ When releasing a dog for hunting, one should recite the takbir (saying “Allahu Akbar”) at the time of release. After that, if the dog is unable to bring the prey back alive to its owner, it is still considered as if it has been slaughtered. If the animal reaches the owner alive, then it should be slaughtered with the recitation of takbir.

Benefits and Issues:

➊ Caution should be exercised in using the utensils of non-Muslims.

➋ The reason for this caution is that those people drink alcohol in their utensils and cook and eat the meat of animals not slaughtered (i.e., carrion) in them.

➌ If it becomes necessary to use such a non-Muslim’s utensil, it should be washed thoroughly or cleaned by scrubbing with earth, then it will be permissible to eat and drink from it.

➍ If a non-Muslim is employed by a Muslim and eats food cooked by Muslims from a Muslim household, then his utensils may also be used after washing them.

➎ If a utensil is not used for storing alcohol but only for water, then it is permissible to drink water from it, even if it belongs to a non-Muslim; however, it should be washed.