Did the Messenger of Allah (peace be upon him) pray two rak'ahs after the Asr prayer? Were they exclusive to him, or for him and his Ummah? And when are they prayed?

The summary of the answer:

Aisha and Umm Salamah mentioned the reason why the Prophet (peace be upon him) prayed two rak'ahs after 'Asr: they were a make-up for the two rak'ahs of the Sunnah of Dhuhr that he missed due to being occupied with the delegation of 'Abd al-Qays. In this hadith there is evidence for the permissibility of making up missed regular Sunnah prayers, the desirability of performing prayers with a specific cause during times when prayer is ordinarily prohibited, and that the Prophet's (peace be upon him) continued performance of this prayer thereafter was one of his unique characteristics.