My replies in blue:
1. Regarding the claim of Fadak, the claim of Fatima (p.b.u.h) was enough because Janabe Fatima (p.b.u.h) is the main spirit of the verse of Tatheer. She would never talk or utter anything which is not true and correct. Under these circumstances, non-acceptance of her claim tantamounted to casting aspersions on Ayat Tatheer wherein God had certified the purity of the characters of the persons of the Cloak.
We disagree with you that purification meant infallibility and we disagree on who this verse was revealed for. So saying that "We Shia are right because Fatimah (as) can never be wrong" This is a weak lazy argument.
2. Why the witnesses of Hazrat Ali (p.b.u.h) and others were not accepted when the Holy Prophet (p.b.u.h) had repeatedly said, “Wherever Ali (p.b.u.h) goes, Truth goes with him.” Ayat Tatheer was revealed in connection with Hazrat Imam Hasan and Imam Husain (p.b.u.h). Were not these two princes, the leaders of the youths of Paradise? Why the witness of Umme Salma, may God be pleased with her, and Umme Aiman, was not accepted even thought they were among those promised paradise by the Holy Prophet (p.b.u.h)? Whether the Qur’an for giving witness was not complete? No, because the witness of two men and one woman or two women and one man was enough to complete the Qur’an. Were the witnesses not the upholders of justice? Leave alone the question of being upholders of justice, their infallibility personified.
The event of the witnesses is a fabricated story by some Koufans and even if it were Sahih Abu Bakr's judgement would still be sound and if they cannot provide more than two female witnesses to prove that a giant piece of land belongs to them, not even documents, then that makes absolutely no sense and is very suspicious.
3. Before arriving at the decision, the wtinessess of Janabe Fatima (p.b.u.h) were driven out. Why? Whther this act was not to be construed as tyrannical or that of high-handedness?
Because this event never took place.
4. This is an undisputed act of Muslim Law that whoever is in possession of anything, be it a property or anything else, it belongs to the person who is possessing it. He would simply say under the oath that a certain property belongs to him. Moreover, witnesses are required by the party who is claiming and not by the one who is having the property in his possession. Under this law calling for witness does not conform with the requirements of Justice. Thus, calling for witnesses from Fatima Zahra (p.b.u.h) was not right. Her responsibility was to simply say an oath. Presenting witnesses was the duty of the first Caliph. Why then Islamic law was tampered with and circumvented?
Fatimah (as) herself refutes your claim since it's authentically and popularly established that she asked for it as inheritance, she did not claim it to be her possession.
5. On many occasions, the first Caliph had agreed to the problems presented by the companions of Prophet (p.b.u.h) without calling for witnesses. For instance, once Janab Jabir came to the Caliph saying that the Prophet (p.b.u.h) had promised that he would pay him some amount.
The first Caliph paid him one thousand five hundred dirhams without calling for witnesses. Similarly, once Abu Basheer Maazani had said that the Prophet (p.b.u.h) had promised to pray him some amount. The Caliph paid him 1400 dirhams (Sahih Bukhari).
Then what was the reason, that in these cases no witnesses were called for. In some cases only companionship of Prophet (p.b.u.h) was enough for consideration. But, in the case of the Prophet’s daughter why witnesses were required? There were the very persons about whom the verse of Tatheer was revealed.
The fact that Abu Bakr helped the Companions and fulfilled the Prophet's (saw) promises is evidence that he was honest and sincere, thus your claims against him are baseless.
6. When Fadak was not considered as a property of Fatima (p.b.u.h), why then on previous occasion the first Caliph had issued a certificate of property in her favour, when earlier she had represented in the matter? Why then the second Caliph seeing the certificate in the hands of Fatima (p.b.u.h) had torn it into pieces and had spat on it? (Sharh Nahjul Balagha, of Ibn Abil Hadeed vol. 16, p.174; Seera Halbiya, vol. 3, p.362)
When Fadak was not the property of Janabe Fatima (p.b.u.h), why was it given to her in the first instance? And if at all it was hers, why was it usurped?
This is a fabricated story that has no sound chain, it contradicts your above story of witnesses, the source quoted by yourself is a non-Sunni one. As for al-Seerah al-Halabiyyah, it mentions that she asked for it as inheritance and it mentions that Abu Bakr told her the narration and it also mentions that `Umar bin `Abdul-`Aziz returned the land to be a Sadaqah just as it was in the Prophet's (saw) time. Here are the texts:
ولما مات صلى الله عليه وسلم وولى أبو بكر رضى الله عنه الخلافة سألته فاطمة رضى الله عنها أن يجعلها أو نصفها لها فأبى وروى لها أنه صلى الله عليه وسلم قال إنا معاشر الأنبياء لا نورث ما تركناه صدقة أى على المسلمين
فلما صارت الخلافة لعمر بن عبد العزيز رضى اله عنه فقيل له إن مروان اقتطعها أى جعلها أقطاعا له فقال أرأيتم أمرا منعه رسول الله صلى الله عليه وسلم فاطمة أى بقوله صلى الله عليه وسلم لا نورث ما تركناه صدقة ليس لى بحق وإنى أشهدكم أنى قد رددتها على ماكانت على عهد رسول الله صلى الله عليه وسلم أى صدقة على المسلمين
As for your story, it's not a part of the author's words rather he was quoting Sabt-ibn-al-Jawzi who is a rejected deviant:
وفى كلام سبط ابن الجوزى رحمه الله أنه رضي الله تعالى عنه كتب لها بفدك ودخل عليه عمررضى الله تعالى عنه فقال ما هذا فقال كتاب كتبته فاطمه بميراثها من ابيها فقال مماذا تنفق على المسلمين وقد حار بتك العرب كما ترى ثم احذ عمر الكتاب فشقه
7. If the first Caliph was right in the case of Fadak, then why did he repeatedly repent at the time of remembering Fadak? And why he himself was ashamed of his own act?
Where's the evidence that he repented because his decision on Fadak was wrong? Also we can bring authentic evidence that `Ali regretted his wars in Jamal and Siffeen, does this mean he was wrong?
8. The hadith that was quoted by the first Caliph for not conceding Fadak was clearly against the spirit of the Qur’an. In Qur’an, there is reference to the property of Sulaiman, Dawood, ‘Aal-e-Yaqub, Zacharia and Yahya – all of them were prophets and property holders (Surah Naml, verse 16; Surah Mariam, verse 46).
Apart from the above, Janabe Fatima Zahra (p.b.u.h) was infallible, virtue and honest. Why then her statement was not taken as true? The hadith recited by the first Caliph was not conforming with Qur’anic spirit and teachings, and hence, cannot be accepted. Why then was Fatima Zahra (p.b.u.h) deprived and denied her own property?
1-The authentic narration from Abu Bakr does not necessarily state that all prophets do not leave inheritance. (So referring to other prophets serves no purpose).
2-The inheritance in the Qur'an is that of prophet-hood and knowledge and not money. (So it doesn't apply to your situation)
9. If it is true, that the Messenger of Allah had not let any property and if at all there is any, it belongs to the government or to all Muslims, why then the wives of the Prophet (p.b.u.h) specially Abu Bakr’s daughter, Ayesha, were not told to vacate possession of their premises? This was also the property left by the Prophet (p.b.u.h). Whether the denial of the right of property was applicable only to Janabe Fatima Zahra(p.b.u.h)?
Because he (saw) had given them those houses to live in since they cannot remarry after him and several other reasons but this is sufficient.
10. If the property left by the Holy Prophet (p.b.u.h), does not belong to any particular person, then why did Abu Bakr seek permission only from his own daughter, Ayesha, for getting buried besides the Prophet (p.b.u.h)?
If at all the inheritance of property is considered, the wives are not entitled to get a share in it. At the most they can have residential rights. If the property rights are accepted, in the presence of children, a wife’s share is only 1/8th. And in this very 1/8th only, all wives would get equal share. If it is to be distributed among nine wives, the share of each wife would come to 1/72. In this way, Ummul Mo’mineen, Ayesha could give permission only upto her own share. Why other were not approached and consulted?
Because it was her house, she does whatever she wants.
11. If it is accepted that the Holy Prophet (p.b.u.h) did not gift Fadak to Janabe Fatima (p.b.u.h) and that there was no property belonging to the Holy Prophet (p.b.u.h), even then, why were the Ahlul Bayt deprived of the Khums of the Khaibar and the wars? Has Qur’an not ordained to pay Khums to all your relatives (Zul Qurba) (Surah Tawba: 41, Surah Isra: 28)? In regards to booty, the question of inheritance does not arise.
Are you accusing the Prophet (saw) of depriving them of their right? Because you said this Khums was from the Khaybar wars during the life of the Prophet (saw) therefore it was his responsibility (saw) to divide and give each his share.
12. Had the argument and the stand of the Khilafat been right regarding Fadak, then why Omar II, Omar bin Abdul Aziz, Omavi, Saffah, Mehdi and Mamoon Abbasi, had made offers to return Fadak to the progeny of Janabe Fatima (p.b.u.h)?
Just above in the sources you quoted (Seerah Halabiyyah) it says the opposite, that `Umar II returned it as a Sadaqah just as it was, he didn't give it to Fatimah (as).