Regarding the niqab, what are the hadiths and verses pertaining to it?

The correct view is that a woman must cover her entire body, including her face and hands. This is the madhhab (school of thought) of Imam Ahmad and Malik. The evidence for this includes verses from the Holy Quran, such as the Almighty’s saying: ﴿O Prophet, tell your wives and your daughters and the women of the believers to draw over themselves their outer garments.﴾ And His saying: ﴿And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to draw their headcovers over their bosoms.﴾ This is also supported by noble prophetic hadiths, such as Aisha’s hadith concerning Ihram, and the hadith "Woman is 'awrah (i.e., her whole body is to be covered)."