Peace be upon you.
Regarding your first question: It is indeed a teaching of Islam to support the allies of God and to disassociate from His enemies. A true believer takes a correct stance against the oppressors who attack God's religion and the prophets.
For your second question: Mourning through actions like striking the face or chest is a recognized way to express grief, especially for significant figures. There is no issue in adopting this or other forms of mourning for the Ahl al-Bayt, as long as it does not lead to harm or is deemed inappropriate by religious authorities.
As for your third question about the incident involving Fatimah al-Zahra, it is a historical event with doctrinal significance, well-documented in various Islamic historical texts. You can refer to sources like:
- Al-Tabari's History, Volume 2, Page 443, which recounts Umar's confrontation with Ali and others.
- Kanz al-Ummal, Volume 5, Page 651, discussing the aftermath of Abu Bakr's appointment.
- Al-Tabari's History, Volume 2, Page 619, where Abu Bakr expresses regret over revealing Fatimah's house.
Regarding why Imam Ali did not claim the caliphate, it is a complex issue. Initially, he was preoccupied with the Prophet's burial. In subsequent instances, the acceptance of leadership is not solely based on intelligence or bravery but also on the people's readiness to accept the truth and reject falsehood. The Ahl al-Bayt, especially Imam Ali, did not resort to cunning to attain leadership but rather aimed to hold people accountable for supporting the truth.
May you be guided to all that is good.