Is a supplication suspended between the heaven and the earth, neither rising nor being accepted unless prayers and peace are invoked upon the Prophet, peace and blessings be upon him? And has a hadith been narrated to this effect?

There is no Hadith stating that supplications are not elevated or accepted except by sending blessings upon the Prophet, peace and blessings be upon him. However, among the manners of supplication and reasons for its acceptance is that it should begin and end with the remembrance of Allah and sending blessings upon the Prophet, peace and blessings be upon him.