Which Surahs must be recited in Witr?

Also, should one recite a Surah in the 3rd rak'ah of Witr if he performs all the 3 rak’ah at a stretch?

Regarding the witr, what is proven from the Prophet (ﷺ) is that he used to recite al-A’la and al-Kaafiroon and al-Ikhlaas. It was narrated from Abu Dawood (1423), al-Nasaa’i (1736) and Ibn Maajah (1171 – this version was narrated by him – that Ubayy ibn Ka’b (radiAllahu anhu) said:

The Messenger of Allaah (ﷺ) used to pray Witr and recite Sabbih ismi Rabbika al-A’la (al-A’la 87), Qul yaa ayyhu’l-kaafiroon (al-Kaafiroon 109) and Qul Huwa Allaahu ahad (al-Ikhlaas 112). [Classed as saheeh by al-Albaani in Saheeh al-Nasaa’i][1]

Yes, you can recite the Surah in that situation.

Reference:

[1] http://islamqa.info/en/46544