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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
We start by saying that there are three different neighboring places that require being distinguished from one another. These are Namirah, ‘Uranah, and ‘Arafah. The Prophet, sallallaahu ‘alayhi wa sallam, during the Farewell Pilgrimage, first camped at Namirah, then moved from it to ‘Uranah, addressing the people and praying there, and then he moved to ‘Arafah.
Ibn Al-Qayyim said in Zaad Al-Ma‘aad: "He, sallallaahu ‘alayhi wa sallam, camped at Namirah, gave a Khutbah (sermon) at ‘Uranah, and stood at ‘Arafah."
Shaykh Al-Islam Ibn Taymiyyah said in Majmoo‘ Al-Fataawa: "A tent was erected for him at Namirah and that is where his rightly-guided Caliphs would camp after his time. There are markets, rest areas, places to eat, and so forth. When the sun passed its zenith, he and those with him mounted and rode to the prayer area at the base of ‘Uranah, where the Masjid was built, and that is neither a part of the Haram nor part of ‘Arafah."
Ibn Taymiyyah also explained that ‘Uranah is outside of Namirah, as he said: "Namirah is outside of ‘Uranah, on its southwest side."
However, considering the proximity of Namirah to ‘Uranah, some of the jurists regarded them as one place. It is stated in Minah Al-Jaleel (a Maaliki book) that: "Namirah is a valley between the Haram and ‘Arafah; and it is also called ‘Uranah."
We conclude from the above that the Masjid was built in ‘Uranah and that it is called, due to its proximity, Masjid Namirah. It is also known that a part of it is inside the boundaries of ‘Arafah, just as part of it is outside the boundaries of ‘Arafah. This has been clearly marked with signs both inside and outside the Masjid itself, since ‘Uranah – the site of this Masjid – is not part of ‘Arafah according to most of the scholars.
An-Nawawi said: "‘Uranah is not part of the land of ‘Arafah according to Ash-Shaafi‘i and all other scholars, except for Maalik who said it is a part of ‘Arafah."
If this clears things up, then the phrase that you found problematic, i.e., “which is a wadi or valley between Namirah and ‘Arafah” is a correct statement without objection, as the Masjid is at ‘Uranah in reality. This Masjid was built during the time of the ‘Abbaasiyyah (Abbaasid) state. It was called Masjid Ibraaheem. Shaykh Al-Islam Ibn Taymiyyah said: "Then they proceed from it toward the base of the valley, which is the site where the Prophet, sallallaahu ‘alayhi wa sallam, prayed Thuhr and ‘Asr, and he gave a Khutbah while on the border of ‘Arafah at the base of ‘Uranah. There is a Masjid there called the Masjid of Ibraaheem and it was built at the beginning of the Banu Al-‘Abbaas era. So Thuhr and ‘Asr are prayed there with Qasr [shortening the prayers to only two Rak‘ahs each], just as the Prophet, sallallaahu ‘alayhi wa sallam, did with all of the pilgrims praying behind him."
Allaah Knows best.