The hadith of a donkey reporting its owner is compiled in the book of ibn Hebban called the scarred people " المجروحين " (2/328) (which means their narration is not thrusworthy) while quoting Muhammad ibn Mazyad abu Ja'afar. And ibn al-Jawzy in his Mawdo'at (555). The hadith is reported by the sahaibi abi Mandhor (May Allah be pleased with him) and shows that this donkey might be part of the war booty of Khaybar and that he died thorw himself in the well of Abu'l-haytham ibn a-Tayhan.
قال أبو حاتم ابنُ حبان : لا أصل لهذا الحديثِ ، وإسنادهُ ليس بشيءٍ . ولا يجوزُ الاحتجاجُ بمحمدِ بنِ مَزْيَد
Ibn Hebban said: This hadith has no origin. And the sanad is worthless. And can't be used to excuse this sheikh (referring Muhammad ibn Mazyad).
The statement of ibn al-Jawzi is already quoted in the answer of GreatBigBore to some extent here is the complete statement:
وقال ابنُ الجوزي : " هذا حديثٌ موضوعٌ فلعن اللهُ واضعهُ ، فإنه لم يقصد إلا القدحَ في الإسلامِ ، والاستهزاءَ به .
May God curse the fabricator of this tradition, because he only intended to insult and to deride Islam.
The hadith was also mentioned by ibn al-Atheer in "Usd al-Ghabah 6/304" when quoting the biography of the sahabi abu Mandhor. And Imam a-Dhabi in "Myzan al-I'tidal 4/34" also quoting Muhammad ibn Mazyad. Ibn Kathir also quoted it in "al-Bidaya wa-Nihaya 6/158" with the statement: That many of the hufadh (of hadith) have refuted this hadith. Among those who declared it as a fabrication or refuted it are scholars like ibn Hajar al-'Asqalani, Imam as-Suyuti, ibn 'Iraq, a-Shwakani, and Sheikh al-Albani.
Ibn Kathir also quoted an other hadith on the authority of Mu'ad ibn Jabal (May Allah be pleased with him), where the donkey said his name was 'Amr ibn ... and the Messenger of Allah (peace be upon him) named him Ya'for. But this one had also several weaknesses, like an incomplete narrator chain and many not trustworthy narrators.
There are other ahadith quoting the name Ya'for but those also have been qualified as da'if.
There are instead sahih ahadith quoting a donkey called 'Ufayr عُفَيْرٌ.
An other source which quotes a donkey speaking to our Messenger (peace be upon him) is one of the four shi'a books al-Kafi 1/184 quoting a statement of Ali ibn abi Talib (May Allah be pleased with him).
But i couldn't find any narration quoting anything about lady Fatima a-Zahara' (May Allah be pleased with her).
And Allah knows best!