Here are the answers to your questions with the will and Permission of Allah (SWT), Insha'Allah
If Imam Ali had no differences with the first three Caliphs, why did he not participate in any battles that took place during their reigns, particularly when Jihad against the Kuffar is deemed a major duty upon the Muslim? If he did not view it as necessary at that time, then why did he during his own Caliphate whilst in his fifties unsheathe his sword and participate in the battles of Jamal, Sifeen and Naharwan?
After the passing away of Sayyidina Nabi (Sallallaho Alaihe Wassallam) many amongst the Senior Sahabah (RA) were retained back in Madina by Khaleefatur-Rasool Abu Bakr As-Sideeq (RA) and DID NOT emerge in Jihad and examples of that are Sayyidina Umar (RA), Sayyidina Usman (RA) and Sayyidina Ali (RA) and many many others. If you want to use the absurd logic that Sayyidina Ali (RA)did not particpate in Jihad because he had some sort of a problem with Khaleefatur-Rasool Abu Bakr As-Sideeq (RA) then the surely the charge is even greater on Sayyidina Umar (RA) by our logic! But this won't stick (Insha'Allah) because by your admission Khaleefatur-Rasool Abu Bakr As-Sideeq (RA) and Sayyidina Umar (RA) were best of companions Sayyidina Ali (RA)
Then we get to the issue of Sayyidina Ali (RA) and the Battle of Jamal and that is because he was the Ameerul-Mumineen of that time so he wanted to personally REFUTE the Fitnah and not air it and the proof is this statement of Sayyidina Ali (RA) to Sayyidina Talha (RA) after the battle:
رحمة الله عليك أبا محمد, يعزّ عليّ أن أراك مجدولاً تحت نجوم السماء, ثم قال: إلى الله أشكو عُجري وبُجري أي سرائري وأحزاني التي تجول في جوفي- والله لوددت إني كنت مت قبل هذا اليوم بعشرين سنة
Abu Muhammad! Allah’s mercy be upon you! It hurts me alot to see you killed under the sky. Than he said : I complain to Allah of my sadness, By God! I wish I had died twenty years ago.[Al bidaya Vol. 7 , p. 247/Mustadrak Hakim Vol. 3, p. 372/Siyyar Aalam al Niba Vol. 1, p. 36/Majma uz Zawaid , Vol. 9, p. 150]
Your entire theory debunked in detail!
Also, why didn't Imam Ali attend the funerals of the three Caliphs who passed away before him even though he was in the city of Madina at the time of all three deaths?
Where did you get this idea from? Where is the evidence?
Furthermore, you claim that Abu Bakr, Umar and Usman were the Holy Prophet's closest friends and companions and that they loved him dearly. Can you then please explain why none of them were present at the Janaza of the Holy Prophet even though they got to know that the Prophet had passed away? Instead, why did Abu Bakr and Umar give preference to attending the meeting at Saqifa to plan the robbing of the leadership of Islam while Ali along with the Bani Hashim and some other truly devoted companions (Ammar, Salman, Miqdad, Abuzar and Bilal) of the Prophet were busy performing the funeral rites?
Your bogus non-nense is based on one narration of Ibn Abi Shaybah (RA) as follows:
حدثنا ابن نمير عن هشام بن عروة عن أبيه أن أبا بكر وعمر لم يشهدا دفن النبي (ص) ، كانا في الانصار فدفن قبل أن يرجعا
If you have half a brain you would instantly figure out that this narration is disconnected! Sayyidina Urwa Ibn Zubair (RA) wasn't even born until the time of Sayyidina Usman (RA) so how could he possibly have attended the funeral of Nabi (Sallallaho Alaihe Wassallam)?
The Janazah Salah of Nabi (Sallallaho Alaihe Wassallam) was performed individually as explained by Shaykh (Mufti) Ebraheem Desai (HA), please read the full answer.
Sayyidina Aisha (RA) refutes your point of view in this authentic naration and proves beyond doubt that the Janazah Salah of Nabi (Sallallaho Alaihe Wassallam) was done individually and everybody did it!
قال ابن عبد البر في الاستيعاب :عن عائشة قالت ما علمنا بدفن رسول الله ( ص ) حتى سمعنا صوت المساحي من جوف الليل .وصلى عليه علي والعباس وبنو هاشم ثم دخل المهاجرون ، ثم الانصار ، ثم النساء والغلمان الاستيعاب ج 1 ص 47
This cannot be undone and I am sure it will be greatly appreciated.