Are the four rak'ahs prayed before Asr – instead of before Dhuhr due to time constraints – counted among the twelve rak'ahs that build a house in Paradise, and are the Sunnah prayers performed before or after the Adhan?

Based on the hadiths of Umm Habiba and Aisha, may Allah be pleased with them both, whoever prays twelve rak'ahs of supererogatory prayers (nafl) during the day and night, a house will be built for him in Paradise. These rak'ahs are: four rak'ahs before Dhuhr, two rak'ahs after Dhuhr, two rak'ahs after Maghrib, two rak'ahs after Isha, and two rak'ahs before Fajr. It is hoped that the reward will be attained by whoever misses these rak'ahs at their prescribed time and then makes them up, due to the Prophet's (peace be upon him) saying: "If a servant falls ill or travels, what he used to do when he was healthy and resident will be written for him." The time for performing the regular sunnah prayers begins with the entry of the time for the obligatory prayer.