Can someone please explain the Fadak situation to me. From what I understand, Fatima requested that Abu Bakr pass the land of Fadak onto her but Abu Bakr refused because he claimed that the Prophet had told him that Prophets do not leave inheritance. Am I missing any background to this story or is it just that simple?
Why didn't Fatima trust Abu Bakr and why did she die angry with him because of this as the narration in Bukhari says?
Yes, pretty much.
Al Abbas and her both go to Abu Bakr asking for Fadak, assuming that they would both inherit it.
Instead, Abu Bakr would not give it to them. He continued what the Prophet peace be upon him did, which was to split profits made from Fadak upon Bani Hashim. So, no, Abu Bakr did not use Fadak for his own financial gain.
All these details can be found in Al Bukhari, however, these details are usually ignored by Shias that would rather prefer on the issue of Fatima being angry.
In regards to her anger, the narration in Al Bukhari says, "HE SAID: She stayed angry until she died."
The question is: Who is "HE?"
This is an intruiging question since the narrator of the report is A'isha, so it should say, "She said."
Sunni scholars hold the view that "He" is Al Zuhri, who never met Fatima, which makes the hadith disconnected.