Does the Prophet hear our salam? Can he reply back?
Not only does he do both but even our actions are known to him....
I've underlined the chain of narration as well, due the fact these hadith are so strong and accepted by the Ulimah.
It is reported from Ibn mas’ud r.a. that the Prophet s.a.w. said : ” My life is a great good for you, you will relate about me and it will be related to you, and my death is a great good for you, your actions will be presented to me, and if I see goodness I will praise Allah, and if I see evil I will ask forgiveness of Him for you.”
This hadith has been narrated from Ibn Mas’ud by Al-Bazzar in his Musnad(1:397) with a chain declared sound by Imam Al-Suyuti in Manahil Al-Safa (pg.31, #8), Ibn Hajar Al-Haytami in Majma’ Al-Zawa’id (9:24 #91), Al-Iraqi in Tarh al-Tathrib (3:297), Al-Munawi in Fayd Al-Qadir (3:401), Al-Khafaji and Al-Qari in Sharh Al-Shifa’ (1:102) and others.
It is narrated by Ibn Al-Mubarak who said : One of the Ansar narrated to us from al-Minhal ibn ‘Amr that the latter hears Sa’id ibn Al-Musayyib say :”Not one day passes except the Prophet’s s.a.w. community is shown to him morning and evening. He knows them by their marks and their actions, thereby giving witness concerning them. Allah said,”But how (will it be with them) when we bring of every people a witness, and we bring you (O Muhammad) as witness against these?”(4:41)
Narrated by Ibn Al-Mubarak in al-Zuhd(pg. 42), Ibn kathir in his Tafsir 1:500, al-Qurtubi in is al-Tadhkira (1:335), Ibn Hajar Al-Asqalani in Fath Al-Bari (9:99) and Al-Mubarakfuri in Tuhfa al-Ahwadhi (8:300)
Just as an additional information, the hadith quoted by Salih Munajjid which he declared hasan is actually sahih. The hadith is thus :
It is narrated by Abu Dawud with a sound chain as stated by Al-Subki that Abu Hurairah r.a. reported that the Prophet s.a.w. said : No one greets me except that Allah has returned my soul to me so that I may greet him back.”
The hadith has also been declared sahih by Al-Hafidh Imam Al-Nawawi in Riyadh Al-Saliheen and Al-Adhkar. It has also been narrated with sahih chains by Imam Ahmad in his Musnad and by Imam Al-Bayhaqi in Al-Sunan Al-Kubra (5:245 # 1040).