What does the Quran say about Caliph and Caliphate?

What does the Quran say about Caliph and Caliphate?

A Caliph خَليفة (Successor) is a person, who replaces the position of someone. That Allah couldn’t go anywhere or die, therefore Adam couldn’t be His caliph. Adam was placed as a caliph on the earth, not for Allah جَاعِلٌ فِي الْاَرْضِ (Quran, al-Baqara 2:30). While there is no wakîl وَكِيلً (Disposer of affairs) for Allah (Quran, al-Isra 17:2), there is no caliph for Him either. The Quran says nothing about a political caliph or caliphate خِلافة‎ , as it’s understood today. For the four successors after Prophet Muhammed the word Amîr al-Mu’minîn أمير المؤمنين (Commander of the Faithful), was used, not caliph.
All humans, thus all men and women without discrimination, are the caliphs of the people on the earth who lived before (Quran, al-A‘raf 7:69, 169; al-An’am 6:165; Fatir 35:39; an-Naml 27:62; Yunus 10:14). The duties of the people who are caliphs are faith (Iman), righteous deeds (amal-as-salih) (Quran, an-Nour 24:55), to judge honestly, and not to follow the desires (Quran, Sad 38:26) and not to spread corruption (Quran, al-Araf 7:74).