Fatima (A) acquired her divine knowledge

Fatima (A) acquired her divine knowledge from the clear spring of Prophethood and received the excellence of truth from the house of revelation. So her attentive heart was embellished with wisdom and her brilliant reason together with her brightness realized to the fullest extent the real meaning of every fact.
Yet, despite the fact that Fatima heard an abundant volume of narrations from her father what has been reported on her authority is limited to certain issues. The reason for this will be explained later.
Among the narrations reported on Fatima's account are: 
1. Bihar, Chapter??Knowledge.
Imam Askari (A) said: "A woman came to Fatima Zahra (A) and said: `I have a weak mother who has become confused about a matter related to her prayer; she sent me to inquire from you about it.'
Fatima Zahra (A) answered her; the woman repeatedly came with questions for Fatima, and she (A) kindly answered her every time. One day the lady again approached Fatima (A) with another question from her mother and said to Fatima: 
`I shall not inconvenience you (any more), daughter of Allah's Messenger.'
Fatima replied: ‘Ask me regarding anything, which comes to your mind. Because if a man had been hired to transport a heavy load to the top of a mountain for a reward of one thousand dinars, do you think it would bother him?'
The woman said: `No'
Fatima continued: `My reward for (answering) every inquiry is more than that which fills (the space) between the ground and the Throne with pearls; thus, I should be more apt to answer your questions. Surely I heard my father say:
`When the scholars of our Shiite (followers) are gathered (on the Day of Resurrection), they will be bestowed with garments of honor equal in quantity to their knowledge and struggle to guide Allah's worshippers, up to the point that anyone of them will be gifted with one million garments of light.' Then the caller of our Exalted and Glorified Lord will say:
`O you guardians of the orphans of Muhammad. (You) who inspire them when they are separated from their fathers, who are their Imams; these are your pupils and the orphans whom you guarded and inspired, therefore bestow them with garments of knowledge in life. Thus, they will bestow each orphan with that which corresponds to the amount of knowledge he received from them (the scholars); up to the point that some orphans are bestowed with one million garments. Like?so, the orphans bestow those who learnt from them.' Then Allah, the Exalted said:
`Repeat upon these scholars, the guardians of the orphans, the bestowment and double and complete it for them and for those who follow them”
Fatima (A) then added:
`Worshipper of Allah, surely a thread of those garments is better than that on which the sun rises. "'
2. Bihar v.10:
Yazid Ibn Abdulmalik (Nawfali) quoted his father, who quoted his grandfather as saying: 
"Once, I entered the house of Fatima (A) who was the first to greet me; she then said: 
`What brings you here?'
I said: “I have come in search of blessing.”
Fatima then said: “My father (who was present) said: ‘He who greets him or me for three consecutive days, will be granted Paradise by Allah.'
I said: `While you are living?'
She answered: ‘yes, and after we are dead.’”
3. Kashf al Ghumma:
Imam Ali (A) quoted Fatima as saying:
"The Messenger of Allah (S) said: 'Fatima, he who praises you, will be forgiven by Allah; Who will make him my companion where ever in Paradise I may be."
4. Da'awat Ar Rawandi:
Swaid Ibn Ghafla said:
"Once, Ali (A) was inflicted with hardship; so Fatima (A) knocked on the Messenger of Allah's door, who said:
`I hear the movement of my beloved one near the door, Umme Ayman get up and see!'
Umme Ayman opened the door and Fatima entered the house. 
The Prophet then said: ‘You have come to us at a time that you have not previously come!'
Fatima said: `Messenger of Allah, what is the angels food near our Lord?'
The Messenger of Allah said: `By Him Who holds my soul in His hand, fire has not been lit (in our house) for a whole month; yet, I will teach you five statements which Gabriel taught me.'
She (A) said: `Messenger of Allah, what are these five statements?'
The Prophet (S) said: `O Lord of the First and Last; 
O You Possessor of Might, and Strength; 
O You Who is Merciful with the poor;
O You most Beneficent, most Merciful. "'
(Note: It appears as if the fifth statement has been mistakenly erased.) 
Thereafter Fatima returned and Ali (A) saw her and exclaimed:
"May my father and mother be your sacrifice, Fatima; what have you to tell me?"
She said: "I went seeking worldly things, but have returned (with the goodness of) the hereafter.”
Ali (A) then said: "Expect goodness, expect goodness!"
5. Bihar v.10: It is reported in Al?Kafi that Imam Sadiq (A) said:
‘Once, Fatima approached Allah's Messenger with a problem. The Prophet listened to her problem and gave her a wrapped piece of material and said: `Learn that which is written in it.' (When she opened it) she found written in it:
“He who believes in Allah and the Last Day, shall not harm his neighbor.
He who believes in Allah and the Last Day, shall honor his guest.
He who believes in Allah and the Last Day shall say that which is useful or keep silent.’"

Source:
Fatima (A.S.) The Gracious
Abu Muhammad Ordoni