What is the ruling on insulting while angry and then seeking forgiveness, and is it recorded as a sin? And were the Companions who insulted the polytheists sinning or rewarded?

Insulting the deities of polytheists is permissible, rather it is an act of obedience, unless it leads to a greater harm, due to the Almighty’s saying: "And do not insult those they invoke other than Allah, lest they insult Allah in enmity without knowledge." Al-Razi and Ibn al-Jawzi have explained that the prohibition of insulting the deities of polytheists applies if it leads to insulting Allah and His Messenger, or alienating them from accepting the religion. As for what Umar (may Allah be pleased with him) did in his response to Abu Sufyan, it did not result in harm, and he was rewarded for it.