As ALLAH ALMIGHTY said in HOLY QURAN
"Surely Allah and His Angels send blessings on the Holy Prophet (sallal laahu alaihi wasallam). O you who believe! Send Blessings (Durood) and Salutations (Salaams) on the Prophet with worthy Salutation". (Surah al-Ahzab: 56)
and PROPHET MUHAMMAD Sallallaho Alaihi Wasallam SAID
“On Fridays recite the Salawat for me repeatedly ! The Salawat will be conveyed to me." (Ibn Habbaan, Ibn Maaja, Abu Dawood)
Hadhrat 'Abd ar-Rahman bin 'Auf (radi allahu 'anhu) says that one day the Holy Prophet (sallallahu 'alaihi wasallam) came and entered a date garden. There he performed a very long prostration. Hadhrat 'Abd ar-Rahman (radi allahu 'anhu) feared that Allah had sent death to him. He drew close to him and began to look at him. The Holy Prophet (sallallahu 'alaihi wasallam) raised his holy head from the prostration and asked what had happened to him, then he disclosed his fear to him. At this, the Holy Prophet (sallallahu 'alaihi wasallam) said Hadhrat Jibra'il ('alaihis salaam) asked whether he should not give him glad tidings that Allah said that He would send blessings to the person who recited the Holy Qur'an on him and peace and security to the person who bade Salutations to him.
and a lot of references you can get from ahadees
to stand and recite darood and salam after prayer in mosque in group is "mustahib" not compulsory if we do this it is good.