Are the four rak'ahs before Asr, mentioned in the Hadith "May Allah have mercy on a person who prays four [rak'ahs] before Asr," to be prayed at home immediately after the Asr Adhan, or in the mosque?

Praying four rak'ahs before Asr is a confirmed Sunnah. It is preferable to pray them at home, based on the general statement of the Prophet, peace and blessings be upon him: "O people, pray in your homes, for the best of prayers is a person's prayer in his home, except for the obligatory prayers." However, there is no harm if they are prayed in the mosque.