Is there a Greatest Name of Allah by which, if He is invoked, He responds immediately and God breaks the norm through it? Is it exclusive to His Awliya (saints/devout servants) only, or for all people? Is it permissible to supplicate to know it?

The Greatest Name of Allah exists. If He is supplicated by it, Allah answers, and if He is asked by it, He gives. Scholars have differed in identifying it, with most of them believing it to be "Allah," followed by "Al-Hayy, Al-Qayyum" (The Ever-Living, The Self-Sustaining). This does not mean breaking the norm with impossibilities, but rather it is an encouragement to supplicate to Allah by His Most Beautiful Names, especially the comprehensive name "Allah," which encompasses all of the Most Beautiful Names. The answering of supplication can be by expediting the request, or by storing up similar good, or by averting similar evil. Knowledge of the Greatest Name is not exclusive to the righteous; rather, any believer can know it. A Muslim should supplicate to Allah by His Most Beautiful Names in general, choosing from them what suits their need.