Does the Prophet hear the salawat (durood) sent to him?

The Beloved Prophet ﷺ hears the salawat (greetings, blessings, durood) sent to him by one who stands close to his grave. Ahl as-Sunnah wal-Jama'ah hold this as part of their belief that he is alive in his grave.

The Beloved Prophet ﷺ said, "Among the most excellent of your days is Friday; On this day Adam peace be upon him was created; On this day shall be the Nafakhah (Trumpet); on it all creation will be swoon. So, send a great dealing of blessing upon me on this day, for your blessings will be presented to me." The Companions asked, "Allah's Messenger ﷺ! how can our blessing be submitted to you, when your body is decayed?" He ﷺ said, "Allah has prohibited the earth from consuming the bodies of the Prophets." [Sunan Ibn Majah 1636]

The Beloved Prophet ﷺ said, "If anyone of you greets me, Allah returns my soul to me and I respond to the greeting." [Sunan Abi Dawud 2041]

In the explanation of the hadith, Imam Jalal ud-din Suyuti rahimahullah wrote, "The word 'radda' means 'ala al-dawam," i.e. permanently, and not temporarily, in other words, Allah does not return the Ruh and take it back, then return it again and then take it back again, but He returned it to the Prophet ﷺ permanently, and the Prophet ﷺ is alive permanently. [as-Suyuti, al-Hawi lil-Fatawi 2/271-272]