Will the one who calls to God intercede for everyone he knows on the Day of Resurrection, and has there been any evidence for that?

There is no evidence for the right of an invoker to intercede for everyone he knows, nor for the intercession of a Hafiz of the Quran in particular. However, the intercession of some believers for others has been established, as in the Hadith: "A man who is not a prophet will enter Paradise through intercession, (a number of people) like the two tribes of Rabee'ah and Mudar," and in the Qudsi Hadith: "The angels have interceded, the prophets will intercede, and the believers have interceded."