What is the ruling on saying "my dear friend," knowing that "the Dear One" (Al-Aziz) is one of Allah's names, and what is the ruling on saying "For your sake, O City of Prayer, I pray"?

"Al-Aziz" is a name shared by both the Creator and the created, so there is no harm in naming a creature with it. As for the statement, "May Allah bless this city" (Sallallahu 'ala hadhihil madinah), it appears there is no harm in it if what is intended is supplication for it, because "salat" (prayer) in the Arabic language means supplication, as in His (Allah's) saying, the Most High: "And invoke [Allah's blessings] upon them; indeed, your invocations are a source of comfort for them" (Quran 9:103), and the Prophet's (peace be upon him) saying: "And if he is fasting, then let him pray [for you]."