How did the Noble Fatimah (A.S) die? Is it true that Umar ibn al-Khatab accidentally
killed her?

Fatimah’s death was brought about by attempts to coerce the Noble household to pay allegiance to the person some had proclaimed khalif and successor to the Prophet (PBUH).
When Imam Ali (A.S) declined to pay allegiance, Umar ibn al-Khatab brought flaming torches threatening to raze his house to the ground if Ali (A.S) continued to withhold his support.