Tirmidhi

1:
The preferred narration is that of Bilal radi Allahu anhu, because from it the performance of prayer inside the Ka'bah is established.
As for the negation by Ibn Abbas radi Allahu anhuma,
then this negation is based on his own knowledge, because Usamah bin Zayd radi Allahu anhuma had informed him of this, and the reason for Usamah's denial is that when these people entered the Ka'bah, they closed the door and became engaged in remembrance and supplication. When Usamah saw that the Prophet sallallahu alayhi wa sallam was engaged in supplication, he too went to a corner and became absorbed in supplication.
The Prophet sallallahu alayhi wa sallam was in another corner, and Bilal radi Allahu anhu was close to him and was between the two of them.
Since the prayer of the Prophet sallallahu alayhi wa sallam was very light, and Usamah himself was absorbed and engrossed in remembrance and supplication, and Bilal was standing between him and the Prophet sallallahu alayhi wa sallam, it is possible that Usamah was not aware of the Prophet's performance of prayer, and on this basis he denied it.
And Allah knows best.

Hadith Commentary:
Abdul Hameed bin Mahmood narrates that we prayed behind an amir (leader). People compelled us, so we prayed between two pillars. After the prayer, Anas bin Malik radi Allahu anhu said that during the time of the Messenger of Allah sallallahu alayhi wa sallam, we used to try to avoid this. (Jami‘ at-Tirmidhi, Kitab as-Salat, Hadith: 229)

Similarly, Qurrah bin Iyas Muzani narrates that during the time of the Messenger of Allah sallallahu alayhi wa sallam, we were forbidden from forming rows between pillars, and we were strictly prevented from this. (Sunan Ibn Majah, Iqamat as-Salawat, Hadith: 1002)

From these narrations, it is understood that praying between pillars is prohibited.

Imam Bukhari rahimahullah, by adding the restriction of "non-congregational" in the chapter heading, clarified that this prohibition pertains to congregational prayer; if someone is praying alone, then there is no significant harm in it.

For this, he presented the practice of the Messenger of Allah sallallahu alayhi wa sallam, that he prayed between two pillars inside the Ka‘bah. Accordingly, Shah Waliullah Muhaddith Dehlawi rahimahullah writes in the commentaries of Bukhari’s chapter headings:

“A person praying alone may pray between pillars; the dislike is only for praying between pillars in the state of congregation.”

Hadith Commentary:
➊
The purpose of Imam Bukhari rahimahullah is to show that it is not necessary to face the Maqam Ibrahim, rather, in every situation during prayer, facing the Ka'bah is required. Thus, in this narration, it is clarified that the Messenger of Allah sallallahu alayhi wa sallam performed two rak‘ahs in front of the Baytullah.
From this, it is understood that the Maqam Ibrahim was behind him.
The Maqam Ibrahim only becomes the qiblah in the specific case where the worshipper places it between himself and the Ka'bah, because in the other three directions, simply facing the Baytullah is sufficient for the prayer to be valid. This shows that the obligation is to face the qiblah, i.e., to face the Baytullah, and it is not necessary to face the Maqam Ibrahim.

➋
In some narrations of Sahih Bukhari, it is mentioned that Abdullah ibn Umar radi Allahu anhu forgot to ask Bilal radi Allahu anhu how many rak‘ahs the Messenger of Allah sallallahu alayhi wa sallam performed inside the Baytullah.
(Sahih al-Bukhari, al-Jihad, Hadith: 2988)
From this narration, it appears that he asked Bilal radi Allahu anhu about the manner (quality) of the prayer, but was unable to ask about the quantity (number of rak‘ahs). Whereas in the aforementioned narration, it is explicitly stated that Bilal informed him that the Messenger of Allah sallallahu alayhi wa sallam performed two rak‘ahs of prayer. The answer to this is that when Ibn Umar radi Allahu anhu asked, Bilal radi Allahu anhu indicated with two fingers of his hand, from which two rak‘ahs were understood, but they forgot to clarify this verbally, which he used to regret.
And those narrations which negate the performance of prayer inside the Baytullah are less preferred (marjuh), rather, it is established that the Prophet sallallahu alayhi wa sallam did pray inside the Baytullah.
It should be noted that along with the Messenger of Allah sallallahu alayhi wa sallam, Bilal radi Allahu anhu, Usamah radi Allahu anhu, and Uthman ibn Talhah radi Allahu anhu entered the Baytullah.
When Ibn Umar radi Allahu anhu came to know, he was coming out after completing the prayer.
(Fath al-Bari: 1/648)

Takhrij al-Hadith: [وأخرجه البخاري 505، ومسلم 1329، من حديث مالك به]
Jurisprudential Points
➊ Inside the Ka'bah, (whichever direction one faces) prayer is permissible.
➋ In the time of the Messenger of Allah (sallallahu alayhi wa sallam), the House of Allah (Baytullah) had six pillars.
➌ It is permissible for those who are responsible for the administration of the House of Allah (Baytullah) to keep its door closed to the general public.
➍ Taking a narration from a narrator is not taqlid (blind following); otherwise, it would necessitate including the mujtahids among the muqallids.
➎ When both narrators are trustworthy, affirmation takes precedence over negation. For example, if one narrator says that the Messenger of Allah (sallallahu alayhi wa sallam) did not pray inside the Ka'bah, and another narrator says that he did pray inside the Ka'bah, then preference will be given to the latter narrator.
➏ The addition of a trustworthy narrator is acceptable, except when it is contrary to other trustworthy narrators and reconciliation, etc., is not possible.
➐ No matter how great a scholar may be, it is possible that some hadiths remain hidden from him which are known to others; therefore, the belief and practice of blindly abandoning evidences and excessive veneration of men is incorrect.
➑ One should always be in search of the “Sunnah” for acquiring knowledge and for practice.
➒ While praying, the sutrah (barrier) should be at a distance of three handspans.

Benefit:
It is permissible to perform prayer inside the Baytullah (the Ka'bah); in this case, one may face any direction one wishes while praying. The Hatim is also a part of the Baytullah; whoever performs prayer there, it is as if he has prayed inside the Baytullah. Allah Ta'ala granted this humble writer the opportunity to visit His sacred house, the Baytullah, for the first time in June 2013. During this visit, I had the opportunity to pray in the Hatim several times. Insha Allah, at some time in the future, the door of the Baytullah will also be opened, and I will have the opportunity to enter inside and perform prayer there.