Salaam alaykum wa rahmatullah,
Would love to help and I'll do the best I can.
Regarding your first post - all the references that cast doubt on Muawiya - he is wholesale copy-pasting from ShiaPen:
http://www.shiapen.com/comprehensive/muawiya/merits-of-ibn-hind.htmlIn the same article, we see the following citation: "Ibn Abi al Hadeed in Sharh Nahjul Balagha". Ibn Abi al Hadeed, at best, was a Mu'tazili and others have also stated that he was a Shia.
It gets worse when the same article tries to prove Muawiya being a "Nasibi" by quoting, "Lisan al Arab page 762 by Ibn Manzur". Lisan al Arab is a dictionary!
Also, you can see that nearly all of the references come from historical texts but even the crown jewel of historical books, like Tareekh at-Tabari, which he praises, is not 100% authentic. Imam Tabari (rah), in the introduction, admits that not everything in his book is authentic; that he only collected and compiled everything he heard. And he left the task of authenticating each report on the reader. So if that is the case with Tareekh at-Tabari, you can rest assured that the rest of the historical works are prone to the same issue (in many cases, these historical works primarily rely on Tareekh at-Tabari). Therefore, it is upon this Shi'i brother to authenticate his historical references and not doing so, or not being able to do so, questions his competency and does not help his case.
As for "If you see Mu’awiya on my pulpit then kill him", read this:
https://mahajjah.com/if-you-see-muawiyah-on-my-pulpit-then-kill-him/ In short, the report is
mawdu or fabricated.
Moving along, his explanation of 5:55 is extremely problematic for various reasons. The verse says, "Your (real) friends are (no less than) Allah, His Messenger, and the (fellowship of) believers,- those who establish regular prayers and regular charity, and they bow down humbly (in worship)". So they establish prayer, charity and bow down in worship. It
does not say they establish prayer, give charity
WHILE they bow down in worship. Furthermore, notice how the verse says, "THEY", meaning there can be many, not just one.
Regarding the narration itself, it is a fabrication. Please read:
https://islamqa.info/en/answers/112081/the-hadith-ali-may-allah-be-pleased-with-him-gave-his-ring-in-charity-whilst-he-was-bowing-in-prayerUsually in discussions with Shias, I stay away from Muawiya because honestly, I do not love him nor do I dislike him; I am neutral in regards to Muawiya. In fact in doing so (not clinging on to Muawiya), I prove to the Shias that I can concede miles upon miles of territory without damaging the core foundations of Ahlus Sunnah Wal Jama'ah whereas the Shias cannot even give up a centimeter from their side.
To prove that, you should ask him why he, as a Shia, hates Muawiya? After all, his 2nd "infallible" Imam (ra) made peace with Muawiya and abdicated his "Divinely Ordained Wilayah" for Muawiya. Surely, Imam Hassan (ra), as an "infallible", wanted Muawiya to rule which proves that Muawiya's rule was as per Allah's (swt) pleasure, hence, he (Muawiya) was a good man. And if he does not accept that, then ask him if Imam Hassan (ra) made that decision out of his own reason, will and accord which then shatters Imam Hassan's (ra) "infallibility".