I'll try to answer some major points. InshaAllah.
As for the reliability of Ikrimah Mawla Ibn Abbas,
But the scholars of Hadith differed [with one another] in regards to ‘Ikrimah, the slave of Ibn ‘Abbas – and no one else has been more differed upon than him!
It is true that some Imams of Jarh wa Tadeel differed in regards to the reliability of Ikrima. But to say that no one else has been more differed upon than him, is an exaggeration. The fact is that some of them criticized him, while the majority deemed him Trustworthy.
Imaam Bayhaqi said: “Ikrimah is from the Thiqah Thabat people
according to the Majority of A’immah”. [As-Sunan al-Kubra lil Bayhaqi: 8/234].
There are some who elevate him to the status of the most trustworthy and grand narrators [of hadith], and some others who claim he was a liar and accuse him of not being Muslim – for some of his contemporaries have stated that he would not pray. But we don’t want to dive into that topic,
Criticism has been levelled against not just Ikrimah, but against many other Imams as well, which even includes the likes of Imam Bukhari or Imam Jafar as-sadiq, etc. But the thing that should be looked into is that, can that criticism be established and proven against that narrator? Because just because criticism is found against someone won't make him unreliable.
The principle solution in this what Shaykh Nur Al-Deen Itr, a contemporary hadith scholar, explains that one of the reasons in which the criticism of a narrator is accepted is if “
those that strengthen him don’t express why the criticism is inaccurate.”(Manhaj Al-Naqd fi Uloom Al-Hadith, page 100).
In the case of Ikrimah, we find that those who strengthened Ikrimah, rejected the criticism that was made against him.
Haafidh Ibn Hajar al-Asqalaani said: “He is Thiqah Thabat, the Scholar of Tafseer, the accusing of lying on him from Ibn Umar is not proven,
nor is the Bid’ah (of any kind) is proven from him”. [Taqreeb: 4673]
Infact Imam Ibn Hajar refuted all the allegations that were leveled against Ikrimah.
rather we will simply state what Ibn Hibban cited as having been an agreed upon [by consensus/ijma’] maxim, and that is: The narrations/transmissions of an innovator [someone who novels an idea/practice that has no precedence in the Prophetic practice, and also contradicts/rivals it], who promotes and calls [does da’wah] to his innovation, are not accepted if he is the sole transmitter of the narration – especially if there are traces of promotion of his innovation [in the narration] or an indictment of his [theological] opponent [in it].
That's true, but Ikrimah being an innovator isn't authentically proven.
Haafidh Ibn Hajar al-Asqalaani said: “...
nor is the Bid’ah (of any kind) is proven from him”. [Taqreeb: 4673].
There are indeed allegations against ‘Ikrimah, by his contemporaries, for having been aligned with the Khawarij ideology. Among those who stated that about him is Ayyub, the one who narrated this hadith from him. This gives us good enough reason to reject the hadiths which he solely narrates [i.e. reports which he is the sole narrator of], even if we find a corroborating evidence/report for it.
The statement of Imam Ibn Hajar is sufficient to discard the criticism on Ikrima for holding Khariji ideology. As for Ayyub ibn Abi Tamima as-Sakḥtiyani. Then, Let's see the view of Ayyub in regards to Ikrimah.
Imaam Hammaad bin Zayd said that a man said to Ayyoob (As-Sakhtiyaani), “O Abu Bakr, has Ikrimah been accused (of lying)” Ayyoob remained silent, then he said: “As for me, then I do not accuse him” [Tabaqaat al-Kubra: 5/221, Chain Saheeh]
Imaam Ayyoob also said: “The Huffaadh of (the hadeeth of) Ibn Abbaas have unanimously consented upon Ikrimah, among them are: Sa’eed bin Jubayr & Ataa bin Abi Ribaah, they would ask him about the hadeeth of Ibn Abbaas” [Ad-Du’afa al-Kabeer by al-Ukaylee: 3/376, Chain Saheeh]
Imaam Sufyaan ibn Uyaynah said, I heard Ayyoob (as-Sakhtiyaani) saying: “If I were to tell you that Hasan (al-Basari) quit narrating a lot of Tafseer when Ikrimah (the expert of Tafseer) entered upon us in Basrah until he went out of it, then I said the truth” [Ad-Du’afa al-Kabeer by al-Ukaylee: 3/373, Chain Saheeh]
The second defect here is that ‘Ikrimah never knew Imam ‘Ali, and never met him. Therefore, the hadith is munqati’ [cut-off i.e. time-gap between two people in the chain who clearly never met], and the “munqati’” hadith is from among the subcategories of a weak report.
This report is not munqati because Ikrimah is not narrating from Ali(RA) directly, but rather he is narrating from his Master, Ibn Abbas, his reaction over an incident in which Ali(RA) was involved and what occurred in it and after it.
I will now refer to what Ibn Hajar cited in “Fathul Bari” [12: 270], when he said: In the third volume, we narrated the hadith of Abu Tahir al-Mukhlis, through the transmission of ‘Abdullah b. Sharik al-‘Amiri, from his father, who said: It was said to ‘Ali: Indeed here there are a group of people at the door of the mosque claiming that you are their lord! So he called them, and said to them: Woe upon you all! What say you all? They said: You are our lord, our creator, and our sustainer! He said: Woe upon you all! I am a slave just like you. I eat food like you eat, I drink like you drink! If I obey Allah He will reward me if He wills, and if I transgress His commands I fear that He will punish me, so fear Allah and return to Him!
They refused. Then the next day they came to him, and Qanbar came and said: By God! They have gone back to saying those statements. ‘Ali said: Let them in. Then they said those things again for the third time. He said: If you say that I will kill you all in the worst way. They refused. So he said: O Qanbar, bring them through the passage and station them between the door of the Mosque and the palace. Then he said: Dig a pit in the ground! Then he came with firewood and laid it in the pit and started a fire. He said: I will throw you all in it if you do not take back what you’ve stated and return to Allah! They refused to turn to Allah. So they were dropped into it until they all burned. He said: Indeed when I see a detestable deed...a fire broke out and I called it Qanbara.
Ibn Hajar said: This chain is hasan (good).
‘Adab says: [The trustworthiness of] ‘Abdullah b. Sharik al-‘Amiri has been disagreed upon. Ahmad, Ibn Ma’in, Ya’qub b. Sufyan al-Faswiy authenticated him, and ‘Abd al-Rahman b. Mahdi, Ibn Hibban, and Abu’l Fath Al-Azdi [the Shi’i] discredited him. Al-Azdi said: He was Mukhtariyyan [with al-Mukhtar al-Thaqafi’s camp] and a liar.
Ibn Hajar said in “Al-Isaba” [3:383]: ‘Abdullah b. Sharik was with al-Mukhar in Kufa.
I say: Then Ibn Hajar’s judgement of ‘hasan’ for the hadith is built on two factors:
Firstly: Because [the state of] ‘Abdullah b. Sharik is differed upon [some authenticated him and others discredited him], and the chain of a ‘differed upon’ narrator is ‘hasan’ [okay/good] according to him [Ibn Hajar].
Secondly: That the man is a Shi’i but not accused of anything regarding ‘Ali [i.e. Shi’i by virtue of his alignment with al-Mukhtar & not necessarily because of “tashyyu’ of ‘Ali”].
I say: When Abu’l Fath al-Azdi, the Shi’i, calls him [‘Abdullah b. Sharik] a liar, and Ibn Mahdi rejects him [and his narrations], and Ibn Hibban says that he deserves to be rejected, then he is not allowed to be narrated from at all, and the narrations of his which he alone transmits solitarily [fard] are munkar [rejected]. And Allah knows best.
All of this means that ‘Ali never burned anyone, and that those claims are delusional or the libels of ‘Ikrimah the Khariji.
This report can be used a Shawahid for the report narrated by Ikrimah, this Shia initally tried to portray that Ikrimah was alone in narrating it, while when he found out there exists a report free of Ikrima, but with a narrator who is Hasan al hadeeth, he is trying to force down upon him a one sided view, while if seen in a fair perspective, this report is a good Shahid for the hadeeth of Ikrimah, which further strenghtens the authenticity of that report.
Moreover, Ikrima isn't the only person who narrated about this incident, Shias themselves have reported this story in their books.
This is from Rijal al-kashi with a very strong isnad(the page is 107 narration number 171)
حدثني محمد بن قولويه، قال حدثني سعد بن عبد الله، قال حدثنا يعقوب بن يزيد و محمد بن عيسى، عن ابن أبي عمير، عن هشام بن سالم، قال : سمعت أبا عبد الله (عليه السلام) يقول و هو يحدث أصحابه بحديث عبد الله بن سبإ و ما ادعى من الربوبية في أمير المؤمنين علي بن أبي طالب، فقال إنه لما ادعى ذلك فيه استتابه أمير المؤمنين (عليه السلام) فأبى أن يتوب فأحرقه بالنار
also see:
https://shiascans.com/2017/05/12/aqaed/