Have any Shia books said that Fatima (sa) was angry at Ali (as)?

Please reply to the following specious questions and arguments: Have any Shia books said that Fatima (sa) was angry at Ali (as)? Yes. 1- Shaykh Saduq narrates that when Ali (as) wanted to marry Abu Jahl’s daughter, Fatim (sa) and the Messenger of God (S) got angry at him to the extent that he advised him telling: “O Ali, do you not know that Fatima is a piece of me and I am from her. Whoever hurts her, hurts me and whoever hurts me has hurt Allah, and whoever hurts her after my death then it is as if he has hurt her in my lifetime and whoever hurts her in my lifetime then it is as if he has hurt her after my death.” (‘Elal al-Sharaye’ by Ibn Babvayh, p. 185-186). The Prophet (S) said: “Fatima is a part of my flesh and my soul in my body, whatever angers her angers me and whatever pleases her pleases me.” (Behar al-Anwar by Allama Majlisi vol. 27/ 62). 2. Another incident that infuriated Fatima was when she saw Ali’s head in his slave girl’s lap. Upon seeing this incident, Fatima wrapped up her veil, went to her father’s house and complained to him about Ali (as). (Elal al-Sharaye’, p. 163, Haqqul Yaqin by Baqir Majlisi, p. 203 – 204). 3. Please reply to the following question also: Ali Gharavi, one of the prominent Hawzah (Seminary) scholars says: The Prophet’s private part enters hell. It will see hell inevitably because it has copulated with some pagan women. (Kashful Asrar, Musavi, p. 24)
Concise answer

1. The first hadith (tradition) in ‘Elal al-Sharaye’ is regarding a person who lied to Lady Fatima Zahra about Ali seeking the hand of Abul Jahl’s daughter for marriage. In reality, there was no such incident and the false news about Ali bin Abi Talib (as) was spread by his (as) enemies who wanted to create discord between Fatima and Ali, peace be upon them.

The alleged story of Ali bin Abi Talib (as) intending to marry Abu Jahl’s daughter is not conforming the facts and realities in history because Abu Jahl’s daughter resided in Makkah whereas Ali (as) had married Fatima (sa) in Medina and were living there. The fact is that this hadith had been fabricated by the opponents in order to steer public mind from the caliphs to Ali (as). They wanted to direct naïve masses’ attention to Ali (as) rather than to the sufferings and pains which Fatima (sa) received at the hands of the caliphs after the demise of the Prophet (S).

2. When it comes to the second hadith, although it seems apparently that Fatima (sa) was angry at Ali (as), the fact is that firstly several defects are evident in the chain of narration that render it a useless and rejected tradition. Secondly, Imam Ali (as) has not committed any wrong acts in this regard. Thus, even if we assume that there is no defect in the chain of the tradition, Fatima Zahra’s consent had been earned at the end. Thirdly, differences to such an extent also existed among the prophets. For instance, Moses’ sharp words addressed to Harun can be found in the Quran (Ta-Ha, 92-94) and they are indications of their differences.

3. The third narration about the Prophet’s private part is never authen