assalamu alaikum, 1. Is there any specific surahs to be recited after fathiha for the sunnah prayers. 2.For the prayer to greet the masjid also is there any particular surah to be recited after fathiha?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

There is no specific Surah (chapter) that one has to abide by reciting it after Al-Faatihah [the opening chapter of the Quran] neither in an obligatory prayer nor in a supererogatory prayer. Besides, it was not reported – as far as we know – that the Prophet used to abide by the recitation of any particular Surah after Al-Faatihah in the prayer of the salutation to the mosque or any other prayers except at special prayers, like the two Rak’ahs before Fajr prayer [i.e. the Sunnah of Fajr] and the two Rak’ahs that are performed after the Maghrib prayer, as the Prophet used to recite in the first Rak’ah of these two prayers Surah Al-Kaafiroon [Quran 109] and in the second Rak’ah, he used to recite Surah Al-Ikhlaas [Quran 112].

Also, regarding the two Rak’ahs of the Witr prayer, he used to recite Surah Al-A’la [Quran 87] in the first Rak’ah and Surah Al-Kaafiroon [Quran 109] in the second Rak’ah. However, it is only desirable to do so as it is not an obligation to recite anything in the prayer other than the Al-Faatihah. For more benefit, please refer to Fataawa 98754 and 83568.

Allaah Knows best.