Salamunalaykum,
I thank you for your patience, and apologies for the delayed reply. I will answer the first question , and the others when i get time inshAllah.
I believe it is important to consider and understand that shia muslims firmly believe that Ali ibn Abi Talib a.s had a God-given right to succeed Muhammed s.a.w, and that Muhammed s.a.w had appointed him. Thus, we believe those who usurped the Caliphat, by default, wrongly assumed the power of Cilaphat, which belonged to Ali ibn Abi Talib a.s.
Additionally, we believe the ahlulbayt a.s were wronged in other ways. We find in Saheeh Al Bukhari where it states, Fatima a.s, a woman who embodied patience, one of the leaders of the women of paradise, died angry with Abu Bakr, and believed she had a right to Fadak. Irrespective of the arguments you use, or i use, for this issue, it is essential to consider how Ali ibn abi Talib a.s, Ibn Abbas r.a, and Fatima a.s, who were the family of Muhammed s.a.w, who knew fiqh and islamic principles, especially pertaining to their own inheritance far more than anyone else, would even consider claiming something that is not theirs. Put aside that, how it would cause someone not only to stop speaking to Abu Bakr, but to die angry with him.
We find that the root-cause of the instability in Islam, the chaos that emerged, was all due to the seeds sown at the beggining. You see, Uthman Ibn Affan was from the clan of Banu Umayyah. He rose to power after a commitee / shura was carefully chosen by Umar ibn Al Khattab, placing people with clear conflicts of interest who would be biased towards Uthman Ibn Affan, thus leading to his rise.
Uthman Ibn Affan, from the Clan of Banu Umayyah, placed his family above others. He allowed the strength of Banu Umayyah to grow, financially and politically. Muawiyah, the son of the one time great, great enemy of Muhammed s.a.w Abu Sufiyan, were all from the line of Banu Umayyah.
You thus find, Muawiyah being behind many of the wars waged against the ahlulbayt a.s , put aside Jamal, think Siffin, among others. Then look to the treaty with Hasan a.s, where he had to , out of greater good, make a peace treaty with Muawiyah. Ibn Kathir himself records that Muawiyah tried to force Hussain a.s to give his oath of allegiance to his son, Yazid.
Who was Yazid? The man according to many ulema of the ahlus-sunnah, who was a drunkard, played with monkeys, was on the verge of being uninhibited and wrecking the religion, and was the one who ordered the killing, persecution and harm, as well as massacare of companions of Muhammed s.a.w, and his dearest among his ahlulbayt a.s on the plains of Kerbala.
Should shia's, be allowed to thus, believe it was the right of Ali a.s to the caliphat role, and it was wrongly usurped? I see no reason why one can not believe that. It follows automatically, if one disobeys Allah azwj, and hurts the Ahlulbayt a.s, that they by default, hurt Muhammed s.a.w. And one knows that the one who hurts Muhammed s.a.w, hurts Allah azwj. But it all boils down to the original question, and difference on who should have led after, and if i believe Ali as should have led after, and was clearly appointed, those who took it away from them disobeyed the command of Muhammed s.a.w, and that of Allah azwj - by default.
I see no reason why my academic and historical viewpoint on who should have led after the Prophet s.a.w, should be taken as anything more than that, or used to spread fitnah. We differ historically on our view on it, you are entitled to your opinion, me to mine.
As for insulting, and such things, this is the understanding: In Islam, we have the principle of basic Adhab, harmony, unity, and tolerance. As a matter of principle, just because i disagree with someone, it does not mean i begin to abuse them, and start to mock them, it is not really the proper manner in which to engage in a discussion of such a hotly disputed topic.
We find in Nahjul Balagha: "I dislike you starting to abuse them, but if you describe their deeds and recount their situations that would be a better mode of speaking anda more convincing way of arguing" [About Muawiyahs men]
https://www.al-islam.org/nahjul-balagha-part-1-sermons/sermon-206-i-dislike-you-starting-abuse-them Furthermore, in Islam, we have the princple of wanting a United Ummah. Muslims should be brothers and sisters of one another. Therefore, respect must be shown, even if one disagree's with the actions and has a different historical view point on issues, or a different theological view point, they should absolutely recognize the need to respect the symbols of the other madhab, this applies not only to shia's about sunni's, but for sunni's with regards to shia's. If muslims begin to infight, and there is secterianism, wide spread abuse of such highly revered figure's in each school, it will promote bloodshed, intolerance and hate, and cause the entire ummah to erupt, divisions to be even more prominent, and forget shia's being oppressed, it will weaken the ummah as a whole, sunni's or shia's, and strengthen those who neither want shia's not sunni's to exist.
Yes, there is also a principle that shia's are oppressed worldwide. I have family members living in area's where they can't even openly practise their religion. I've been there, and i had to conceal my faith, out of fear of my life and safety. Why would anyone want to promote an act which would allow radicals to continue to spread hatred and intolerance in such a manner?
With regards to asking Allah azwj to remove his mercy, it's forbidden to perform publicly. Whatever anyone does in their home/four walls, is up to them and Allah azwj. If they have commited wrong, Allah azwj will punish them. We find in shariah law, even homosexuality if commited and not brought into public view, is not something we can condemn or prosecute, or punish. I also do not promote, nor have seen in decade(s) anyone promote the l'anah of the caliphs.Suffice to conclude, insulting and abusing the symbols of the ahlus-sunnah is forbidden. That's clear in and of itself. And i believe for someone who revere's the caliphs, they should welcome and promote this ruling, and not those of zealouts who want to abuse them.