Is it required to face the Qibla and be in a state of purity when performing a prostration of recitation (Sajdat al-Tilawah)? And is the prostration of recitation waived when reciting the Qur'an in a vehicle, at the office, or at home?

The Sunnah for someone who passes by a verse of prostration (Ayat al-Sajdah) is to prostrate, emulating the as-Sunnah of the Prophet, peace and blessings be upon him. It is recommended to face the Qiblah if possible. The prostration of recitation (Sajdat al-Tilawah) is not like the prayer (Salat), so it does not require the conditions of prayer, such as ritual purity, because the Prophet, peace and blessings be upon him, did not stipulate that for his Companions. If the reciter is in a moving vehicle, he should prostrate in the direction of travel.