In which references can I find the full account, with chains of narration, of Lady Fatimah's (AS) claim, conversation, and sermons with the first caliph regarding Fadak?
There are many books written on this important subject but not all of them are translated to English. There is a book available on line which was published by Amazon: THE TRAGEDY OF FATIMA DAUGHTER OF THE PROPHET MUHAMMAD, by Allama Sayyid Murtada Al-Amili, translated by Yasin Al-Jibouri.
Also it might be useful for you to see this link
https://en.wikipedia.org/wiki/Umar_at_Fatimah%27s_house
Wassalam.