Okay, so one is to do ijtihad when he does not find judgement regarding the issue/matter he is facing at present in al-Quran and Sunnah. This means that there can be no ijtihad regarding an issue where one can find clear commandments in al-Quran and Sunnah?
If yes, then in al-Quran ALLAH (SWT) has clearly mentioned believers to obey those in authority and if there is disagreement between believers and those in authority then the matter should be referred to ALLAH (SWT) and the Messenger (s.a.w.w). Messenger (s.a.w.w) has clearly commanded believers not to fight Muslim rulers and also not to fight each other both in times of peace and Fitna.
Of course.
Because according to Muawiya such commandments were not judged to be applicable because Allah(swt) gave them permission to fight others if they transgressed upon them:
وَإِن طَائِفَتَانِ مِنَ الْمُؤْمِنِينَ اقْتَتَلُوا فَأَصْلِحُوا بَيْنَهُمَا ۖ فَإِن بَغَتْ إِحْدَاهُمَا عَلَى الْأُخْرَىٰ فَقَاتِلُوا الَّتِي تَبْغِي حَتَّىٰ تَفِيءَ إِلَىٰ أَمْرِ اللَّهِ ۚ فَإِن فَاءَتْ فَأَصْلِحُوا بَيْنَهُمَا بِالْعَدْلِ وَأَقْسِطُوا ۖ إِنَّ اللَّهَ يُحِبُّ الْمُقْسِطِينَ
Sahih International
And if two factions among the believers should fight, then make settlement between the two. But if one of them oppresses the other, then fight against the one that oppresses until it returns to the ordinance of Allah . And if it returns, then make settlement between them in justice and act justly. Indeed, Allah loves those who act justly.
Since Ali and Muawiya didn't fight yet and were still negotiating, being attacked by Ali's army, Muawiya understood Ali's army to be the transgressors and that Allah permitted him to fight back.
Is there any hadith stating this i.e. anyone who has sufficient knowledge in various branches and can perform ijtihad independently.
As of yet I have only seen one hadith where a person can perform ijtihad and that person is Hakam.
Sorry, which narration are you talking about?
Muhajirun and Ansar had given bayah to Imam Ali (a.s) without placing any condition. Muawiya was from Ṭulaqāʾ (Arabic: طُلَقاء) and thus not part of group who were considered decision makers i.e. Muhajirun and Ansar.
Secondly, Battle of Jamal had taken place before Battle of Siffin and opponents of Imam Ali (a.s) regretted taking part in the battle of Jamal after they realized that battle had no positive outcome. They considered Qisas of Uthman to be genuine legal right but after the battle (of Jamal) they saw that it was creating more Fitna as Muslims were divided in two groups and fighting one another.
Muawiya after seeing the aftermaths of Battle of Jamal should had abandoned the condition of Qisas and given bayah to Imam Ali (a.s) in the interest of Muslim Ummah.
Muawiya obviously saw himself as a decision maker because he was a governor under Uthman and held sway over a large part of the population. The decision makers were not only Muhajirun and Ansar, I haven't seen anything explicit about this. The decision makers are those who have enough influence and power over others so that they can cause people to unite and prevent them from descending into anarchy.
Of course, Muawiyah should have never made that condition in the first place, but again we are not talking about what should have happened. Why didn't he, do you ask? First of all, the battle of Jamal occurred because the opponents of Ali moved towards Ali's army. Muawiya never did that and he didn't intend to attack Ali, he only didn't want to pledge allegiance to him. Secondly, some of the opponents of Ali were actually those who pledged allegiance to him, so people who pledged allegiance to Ali were fighting each other and Muawiya may have seen this as another confirmation of Ali, not being able to assert his authority and that this matter had to be dealt with.
If it is as you say so then why did Imam Ali (a.s) not step down from the seat of ruler-ship if he a.s (according to you) was held hostage by his (a.s) own army?
According to me? So I try to prevent speculating about what Muawiya was thinking, but seeing that that is actually what you are interested in and in trying to respond to that interest you return the favor by saying that this according to me?
Anyway, Imam Ali (a.s.) obviously didn't think he was held hostage.
If lot of them died in the battles of al Jamal, Siffin and Nahrawan then what was the reason of Muawiya not giving bayah to newly appointed Caliph i.e. Imam Hassan (a.s)? What was the reason of Muawiya fighting with Imam Hassan (a.s)?
There are a lot of difference's between Ali's Caliphate and al Hassan's
First of all, a lot of them doesn't mean all of them.
Secondly, they themselves may have died but they have created a culture were such rebellious ways were copied by others(who for example killed Ali, robbed and stabbed al Hassan etc.) so they were replaced by people who were equally or more anarchistic. It wasn't just about the murder of Uthman, Muawiya simply distrusted them. The murder of Uthman was a confirmation of that and gave him a legal basis for opposing them. He was generally suspicious of people who could not keep order as he saw them as fitnah makers if given the opportunity. He also saw this as a violation of the Prophet's command to keep the Caliphate to the Quraysh, which according to him probably didn't only mean the Caliph himself but the entire power structure as others would cause fitnah. It was after all his father who wanted to depose Abu Bakr and help Ali. They distrusted lower clans of Quraysh to keep order, let alone bedouins and Egyptians etc. It wasn't as much about Ali or al Hassan as it was about these people.
Thirdly, after Abu Musa al Ashari's blunder, Ali was supposed to have stepped down and therefore Muawiya had a legal basis for being declared Caliph himself. Since Muawiya preceded al Hassan in being declared Caliph, al Hassan's case, according to Muawiya was not so strong.
Fourth, even if Ali was the Caliph, he didn't appoint his son. Shia's may believe so and may even believe that the Prophet (ﷺ) did so, but I don't think there is good evidence from the reports of Sunni's that Ali did.
Fifthly, al Hassan didn't have as much support as Ali (ra). The supporters of Ali in Kufa after Ali's death pledged allegiance to him, but is there evidence that the Muhajirun and Ansar in Medinah did as well? I don't know, I have to double check.
Lastly, by this time, seeing how a part of Ali's army behaved, Muawiya completely lost faith in the competence of Ali to control them and had even less in al Hassan that he could. Remember, al Hassan was wounded by them and robbed him of his possessions. Some accounts go even so far that they took the prayer mat beneath him while he was sitting on it.