Why did Muawiya during the time of Fitna not adhere to a group of Muslims having a Leader as per instructions of the Prophet (s.a.w.w)?
But weren't they (i.e. Sahabas) aware of the Ahadith of Fitnah where Prophet (s.a.w.w) instructed Muslims to adhere to the group of Muslims having a Leader?
Things weren't as simple as you think, this is the reason in a Prophesy of Prophet(saws), he said that, the group that will kill khawarij will be NEAR to truth. Pay attention to the eloquence of Prophet(saws) and his choice of words. He didn't say, the party which kills khawarij would be ON the truth. He used the words "Near the truth", which shows that the other party to had a share of truth, lesser than the other but yet had a share of truth.
Abu Sa'id al-Khudri reported from the Messenger of Allah (ﷺ) that a group (Khawarij) would emerge from the different parties (the party of Hadrat 'Ali and the party of Amir Mu'awiya),
the group nearer the truth between the two would kill them. [Sahih Muslim 1065 e]
The situation that time was such that Uthman(ra) was martyred and those who martyred him infiltrated into the ranks of Shia of Ali(ra). So Muawiya(ra) asked for Qisas, and made this right as a condition, after which he agreed to give allegiance to Ali(ra). On the top of that, there were rumors spreading around that Ali(ra) had a hand in martyrdom of Uthman(ra). And then Ali(ra) kept delaying punishing the killers of Uthman(ra), which made things complicated and Muawiya(ra) considered him to be right in defending himself from the offensive attack in such chaotic situation. He made wrong ijtihad, as Sunnis believe, but he had a portion of truth.
Can you provide me a single hadith where Prophet (s.a.w.w) instructed Muslims to fight back the Ruler of Muslim Ummah when the latter (i.e. Ruler) has waged offensive war against the former (i.e. Muslims)?
Its an invalid question. Because Muawiya(ra) didn't give allegiance to Ali(ra) due his Ijtihad. So him being on defensive falls under this category as well, moreover we know that when your life is in danger, what is haram on you becomes halal in order to protect your life. So even if supposedly being on defensive against the leader was haram, but to protect his life from a leader who is on a wrong stance(as per Muawiya) he committed it considering it becomes legal in such a situation.
You said that Muawiya fought back Imam Ali (a.s) but Tābi 'Abd al-Rahman b. Abd Rabb al-Ka'ba said that Muawiya, "orders us to unjustly consume our wealth among ourselves and to kill one another" and Sahabi Abdullah b. 'Amr b. al-'As instead of refuting 'Abd al-Rahman said to the latter, "Obey him (i.e. Muawiya) in so far as he is obedient to God; and disobey him in matters involving disobedience to God."?
As explained by scholars like Imam Nawawi
المقصود بهذا الكلام أن هذا القائل لما سمع كلام عبد الله بن عمرو بن العاص رضي الله تعالى عنهما، وذكر الحديث في تحريم منازعة الخليفة الأول، وأن الثاني يقتل، فاعتقد هذا القائل هذا الوصف في معاوية؛ لمنازعته عليا رضي الله تعالى عنهما، وكانت قد سبقت بيعة علي، فرأى هذا أن نفقة معاوية علي أجناده، وأتباعه في حرب علي، ومنازعته، ومقاتلته إياه، من أكل المال بالباطل، ومن قتل النفس؛ لأنه قتال بغير حق، فلا يستحق أحد مالا في مقاتلته
(شرح مسلم” 12/ 437. “كتاب الإمارة”.)
And Imam Qurtubi:
واستحلاف عبد الرحمن زيادة في الاستيثاق، لا أنه كذبه، ولا اتهمه. وما ذكره عبد الرحمن عن معاوية رضي الله تعالى عنه إغياء في الكلام على حسب ظنه، وتأويله، وإلا فمعاوية رضي الله تعالى عنه لم يعرف من حاله، ولا من سيرته شيء مما قال له، وإنما هذا كما قالت طائفة من الأعراب: إن ناسا من المصدقين يظلموننا، فسموا أخذ الصدقة ظلما؛ حسب ما وقع لهم
(المفهم 4/53)
The Taba'i narrator when heard the hadeeth from Abdullah bin Amr bin al-aas, about obeying the caliph, who is given caliphate first. He made his own deduction out of it applying to the case of Ali(ra) and Muawiya(ra). In regards to him saying "Muawiya orders us to unjustly consume our wealth among ourselves and to kill one another", he meant that since Ali(ra) was the rightful Caliph, then the wealth that Muawiya(ra) is spending in the war, is like unjust consumption of wealth and is like killing to kill one another. Now this was his personal deduction, whether it was correct or not is a different issue, as explained by Imam Qurtubi, since different people view andd judge things in different manner.