Is translating "The Messenger of Allah, peace and blessings be upon him, said" to "The Messenger, peace and blessings be upon him, kindly said" permissible in Persia, or is it a violation of the Prophet's guidance, peace and blessings be upon him, given that both phrases are found in translated Hadith books?

The word "tafaḍḍal" (تفضل) has two meanings: a customary one and a linguistic one. The customary meaning is politeness and respect, while the linguistic meaning is un-obligatory benevolence or favor. The intent behind using it in the mentioned context is excessive respect. Although this is good, it goes against the methodology of the Companions, the Tabi'un (followers), and the Imams, who would simply say "The Messenger of Allah, peace and blessings be upon him, said" without affectation. This is because they were the most loving and respectful of people. Indeed, goodness lies in following the predecessors, for they did not leave any good trait but hastened to embrace it.