The selection of caliph in the time of Imam Ali

Imam Ali (peace be upon him) objected to the choice of Usman severely:

6. He objected to the caliphate of Usman and tolerated as much as Abd Al-Rahman Ben Uf threatened him to murder
قال عبد الرحمن بن عوف : فلا تجعل یا علی سبیلاً إلى نفسك ، فإنّه السیف لا غیر .
Al-Emamat Al-Siyasat, Researched by: Al-Shiri, v 1 p 45, Researched by: Al-Zeini, v 1 p 31
Umar really moaned and shouted from the story of six person council:
فَیَا لَلَّهِ وَ لِلشُّورَى مَتَى اعْتَرَضَ الرَّیْبُ فِیَّ مَعَ الْأَوَّلِ مِنْهُمْ حَتَّى صِرْتُ أُقْرَنُ إِلَى هَذِهِ النَّظَائِرِ لَكِنِّی أَسْفَفْتُ إِذْ أَسَفُّوا وَ طِرْتُ إِذْ طَارُوا فَصَغَا رَجُلٌ مِنْهُمْ لِضِغْنِهِ وَ مَالَ الآخَرُ لِصِهْرِهِ مَعَ هَنٍ وَ هَنٍ إِلَى أَنْ قَامَ ثَالِثُ الْقَوْمِ نَافِجاً حِضْنَیْهِ بَیْنَ نَثِیلِهِ وَ مُعْتَلَفِهِ وَ قَامَ مَعَهُ بَنُو أَبِیهِ یَخْضَمُونَ مَالَ اللَّهِ خِضْمَةَ الْإِبِلِ نِبْتَةَ الرَّبِیعِ إِلَى أَنِ انْتَكَثَ عَلَیْهِ فَتْلُهُ وَ أَجْهَزَ عَلَیْهِ عَمَلُهُ وَ كَبَتْ بِهِ بِطْنَتُهُ
Rest on God from this council Have I ever been equal with members of the council which I am considered equal with them? I had to regress and to get along with them. One of them that had animosity with me turned me away and the other one prioritized his brother-in-law ( his daughter's husband) and it is right to mention two other persons( Talhe and Zobeir).
When the third person became caliph, he ate a lot and he was always between kitchen and rest room. His paternal relatives from Bani Umaye ate and wasted the properties of Beit Al-Mal. As a hungry camel eats all of plants of spring, he overindulged as much as his actions provoked people and because he was so glutton, he was disintegrated.
Nahaj Al-Balaghe, Sermon 3

Imam Ali (peace be upon him) considered Abu Bakr and Umar betrayer and cheater.

7. Amir Momenan (peace be upon him) Abu Bakr and Umar liar, sinner, cheater and betrayer.
Umar said to Abbas and Ali in the book '' Sahih Mosalam'' that one of the most valid book after the Quran from the point of view of Sunni scientists

فلمّا توفّی رسول اللّه صلى اللّه علیه وآله، قال أبو بكر: أنا ولی رسول اللّه... فرأیتماه كاذباً آثماً غادراً خائناً... ثمّ توفّی أبو بكر فقلت : أنا ولیّ رسول اللّه صلى اللّه علیه وآله، ولی أبی بكر، فرأیتمانی كاذباً آثماً غادراً خائناً ! واللّه یعلم أنّی لصادق، بارّ، تابع للحقّ! .
After the prophet (peace of Allah be upon him and his descendants) claimed the caliphate of Hazrat Muhammad. Both of you (Ali and Abbas) considered Abu Bakr liar, sinner, cheater and betrayer and after Abu Bakr deceased, I claimed the caliphate of the prophet and Abu Bakr , you considered me liar, sinner, cheater and betrayer.
Sahih Moslem, v 5 p 152, (p 728, Hadith 1757), Ketab Al-Jahad chapter15 Hakam Al-Fi Hadith 49, Fataha Al-Bari, v 6 p 144

Imam Ali (peace be upon him) considered last caliphs the usurper of caliphate:

8. Imam Ali (peace be upon him) did not consider any legitimacy for last caliphs and he considered them as usurpers of his right for caliphate as he wrote in his letter to Aghil
فَجَزَتْ قُرَیْشاً عَنِّی الْجَوَازِی فَقَدْ قَطَعُوا رَحِمِی وَ سَلَبُونِی سُلْطَانَ ابْنِ أُمِّی.
Nahaj Al-Balaghe, Ketab no 36
God may torture Ghoreish tribe for their inappropriate deeds because they disconnected my relationship with my relatives and they robbed the government of my mother's child, the prophet (peace of Allah be upon him and his descendants) from me.
It has been said in the narration of Ebn Abi Al-Hadid that Hazrat Ali bade
وغصبونی حقی ، وأجمعوا على منازعتی أمرا كنت أولى به.
The Ghoreish tribe usurped my right and they stood against me for caliphate that I was the most deserved person.
Sharh Nahaj Al-Balaghe Le Ibn Abi Al-Hadid, v 4 p 104, v 9 p 306
According to the remark of Ebn Ghatibe, when Abu Bakr sent Ghanfaz to the presence of Hazrat Ali, he said to him
یدعوكم خلیفة رسول الله (ص)

O' Caliph! The prophet has summoned you.
Hazrat Ali (peace be upon him) answered
لسریع ما كذبتم على رسول الله (ص)
How soon they lied to the prophet (peace of Allah be upon him and his descendants) and they addressed themselves his caliph.
ثمّ قال أبو بكر : عد إلیه فقل : أمیر المؤمنین یدعوكم ، فرفع علی صوته فقال : سبحان الله لقد ادعى ما لیس له .
Abu Bakr sent Ghanfaz to the presence of Imam Ali (peace be upon him) and said '' say to him that Amir Al-Momenin has summoned you. When Imam Ali peace be upon him) heard this remark, he called '' he has had an unexpected claim''.
Al-Emamat Al-Siyasat, Researched by: Al-Zeini, p 19, Al-Shiri, p 30
According to the mentioned seven points, is it to say that Imam Ali (peace be upon him) believes the role of council in caliphate or he considers caliphate of past caliphs legitimate?!

Is the common accord of the companions due to the satisfaction of God?

Hazrat Ali (peace be upon him) bade
فَإِنِ اجْتَمَعُوا عَلَى رَجُلٍ وَ سَمَّوْهُ إِمَاماً كَانَ ذَلِكَ لِلَّهِ رِضًا
If the migrants and the supporters consider someone as their Imam and they address him their Imam, God will be satisfied.
The Sunni scientists cannot reason to the remark of Hazrat Amir (peace be upon him) in order to prove the reality of caliphate of caliphs because
First: in some transcriptions of Nahj Al-Balaghe, instead of sentence
«كَانَ ذَلِكَ لِلَّهِ رِضًا»
«لِلَّهِ» has been said without word «كَانَ ذَلِكَ رِضًا» phrase
Refer to Nahaj Al-balaghe Published in: Egypt, Cairo, Al-Esteghamat. Allah Word is stated in the prantases

In other words, if the migrants and the supporters select someone for caliphate, it will be with their satisfaction and this allegiance has not been done by force and with sword.
Second: suppose that there is this word in the sermon, it means that if all of the migrants and the supporters, Hazrat Ali (peace be upon him), Sedighe Tahere, Imam Hasan (peace be upon him) and Imam Hussein (peace be upon him) are also considered, have common accord about Imamate of a person, it will definitely be the satisfaction of God.

Did Hazrat Fateme (peace be upon her) swear allegiance with Abu Bakr

According to the valid narrations (according to the narration Haken Neisaburi / the messenger of God (peace of Allah be upon him and his descendants) to Hazrat Fateme Zahra (peace be upon her), the satisfaction of Sedighe Tahere was the satisfaction of the prophet and her anger was the anger of the prophet
إنّ اللّه یغضب لغضبك، ویرضى لرضاك.
God will be angry with your anger and God will be satisfied with your satisfaction.
Then he said
هذا حدیث صحیح الإسناد ولم یخرجاه.
This narration is valid, but Bokhari and Mosalam have not mentioned it.
Mostadrak: 3/ 153, Majma AL-Zavaed: 9/ 203, Al-Ahad Al-Mathani Lel Zahak: 5/ 363, Al-Esabat: 8/ 265 266, Tahzib Al-Tahzib: 21/ 392, Sabal Al-Hoda Al-Reshad Lel Salehi Al-Shami: 44/ 11
According to the narration of Bokhari, Hazrat Muhammad (peace of Allah be upon him and his descendants) bade
فاطمة بَضْعَة منّى فمن أغضبها أغضبنی .
Fateme is a part of my body and whoever makes her angry has made me angry.
Sahih Al-Bokhari: 4/ 210, (p 710, Hadith 3714), Ketab Fazael Al-Sahabe, chapter 12, chapter Managheb Gharabat Rasulollah and 4/ 219, (p 717, Hadith 3767), Ketab Fazael Al-Sahabe, chapter 29, chapter Managheb Fateme Alaiha Al-Salam
According to the narration of Neishaburi, Hazrat Muhammad (peace of Allah be upon him and his descendants)
إِنَّمَا فَاطِمَةُ بَضْعَةٌ مِنِّی یُؤْذِینِی مَا آذَاهَا.
Fateme is a part of my body and whoever hurts her has hurt me.
Sahih Moslem 7/ 141, hadith 6202, Ketab Fazael Al-Sahabe Raziollah Taala Anhom, chapter 15, chapter Fazael Fateme Bente Nabi Alaiha Al-Salat Vasalam
There is no question that Hazrat Zahra (peace be upon her) did not only swear allegiance with Abu Bakr , but she also passed away when she was angry and furious of Abu Bakr.
According to the narration of Bokhari,
فَغَضِبَتْ فَاطِمَةُ بِنْتُ رَسُولِ اللَّهِ صلى الله علیه وسلم فَهَجَرَتْ أَبَا بَكْرٍ، فَلَمْ تَزَلْ مُهَاجِرَتَهُ حَتَّى تُوُفِّیَتْ.
Sahih bokhari : 4/ 42, Hadith 3093, Ketab Farz AL-Khoms, chapter 1, Farz AL-Khoms
Hazrat Fateme, the daughter of the messenger of God (peace of Allah be upon him and his descendants) was angry of Abu Bakr and she was not on speaking terms with him until she passed away.
As Hazrat Fateme (peace be upon her) willed, Imam Ali (peace be upon him) buried her at night and he prayed her body without informing Abou Bakr that introduced himself as the caliph of the prophet (peace of Allah be upon him and his descendants)
فَلَمَّا تُوُفِّیَتْ، دَفَنَهَا زَوْجُهَا عَلِیٌّ لَیْلاً، وَلَمْ یُؤْذِنْ بِهَا أَبَا بَكْرٍ وَصَلَّى عَلَیْهَا .
Sahih Bokhari, v 5 p 82, Hadith 4240, Ketab AL-Moghazi, C 38 chapter Ghazvat Kheibar, Sahih Moslem, v 5 p 154, Hadith 4470, Ketab Al-Jahad Al-Seir ( Al-Maghazi), C16 chapter Ghole Al-Nabi Salallah Alaihe Vasalam, ( La Noratho Ma Tarakna Fahova Sadaghat)

Supporters and Did Imam Ali (peace be upon him) have any relationship with the immigrants ?

Didn't Imam refuse to swear allegiance with Abu Bakr for six months according to the narration of Bokhari and Mosalam :
وعاشت بعد النبی صلى الله علیه وسلم، ستة أشهر... ولم یكن یبایع تلك الأشهر .
Hazrat Fateme remained alive for six months after the decease of the prophet and during this time Imam Ali (peace be upon him) did not swear allegiance with Abu Bakr.
Sahih Al-Bokhari v 5 p 82; Sahih Mosalam v 5 p 154
Was not swearing allegiance of Imam Ali (peace be upon him) due to lack of legitimacy of Abu Bakr caliphate?
Didn't Bani Hashem tribe refuse to swear allegiance following Imam Ali (peace be upon him)?
According to the narration of Abd Al-Razagh, the instructor of Bokhari,
فقال رجل للزهری : فلم یبایعه علیّ ستة أشهر ؟ قال : لا ، ولا أحد من بنی هاشم .
Mardi said to Zehri '' wasn't it right that Imam Ali (peace be upon him) did not swear allegiance during six months? He answered '' Imam Ali and no one from Bani Hashem tribe did not swear allegiance during six months?
Al-Mosnef Labod Al-Razagh Al-Sanaani , v 5 p 472- 473
Beihaghi in book '' Sonan'' , Tabari in book '' Tarikh'', and Ebn Asir in two books '' Rejal'' and '' Tarikh'' have narrated such interpretation.
Asad Al-Ghabe, v3/ p 222; Al-Kamel Fi Al-Tarikh v 2 / p 325 and Al-Sonan Al-Kobra, v 6 p 448.
Didn't Ebn Hazam , one of Sunni great scientists, say
ولعنة اللّه على كلّ إجماع یخرج عنه على بن أبى طالب ومن بحضرته من الصحابة .
Al-Mahali: v 9 p 345, Researched by: Ahmad Muhammad Shaker, Beirut, Dar Al-Fekr
Curse to a group that does not include Imam Ali (peace be upon him) and his supporters.