What is "Eshed ha'Nechalim" referring to?
Rashi, Rashbam (by inference) and Targum Yonasan: It is referring to 'the outpouring of the 'streams of blood' of the Emori'im and the Mo'avim'. 1
Ramban and Da'as Zekenim: "Eshed" 2 refers to the inclines along which streams flowed to Ar (all of which Sichon attacked and took 3 from Mo'av).
Seforno: Refer to 21:14:4:3.
Targum Yonasan: It is referring to the flowing of the streams of blood of the B'nei Edom and the B'nei Mo'av. 4
See also answer #4 and Ba'al ha'Turim.
Ramban: As in Devarim 3:17, Yehoshua, 10:40.
Ramban: But not Ar itself.
See also answer #1.
What is the rest of the Pasuk "asher Natah Lasheves Ar ... " referring to?
Rashi and Targum Yonasan: It is referring to the mountains of the Emori 1 which veered towards Ar 2 and leaned towards the border of Mo'av. 3
Seforno: It is referring to the swelling of the rivers and their flowing which reached as far as Ar. 4
Da'as Zekenim and Hadar Zekenim (on Pasuk 14): Initially, the rivers flowing down to Ar on both sides were from Mo'av. Now, the land [to the north] was taken, and the Nachal was the border.
Targum Yonasan: It is referring to the rivers of blood of the B'nei Edom and the B'nei Mo'av, 5 which flowed up to Ar, which was on the border of Mo'av. 6
See also answer #4..
The capital of Mo'av.
The path on which Yisrael were travelling passed through a valley between two mountains close to one another, so that someone standing on one mountain could speak to someone on the other mountain. There were caves in the mountain on the side of Mo'av, and protrusions opposite them on the other mountain on the side of the Emori that fitted like pieces of a jigsaw puzzle. The Emori'im waited in the caves for Yisrael to pass along the path, ready to kill them with arrows and boulders. But Hashem performed a miracle, and, as Yisrael approached, the latter mountains moved, like a maidservant who goes to greet her mistress, and the protrusion entered into the caves, killing the Emori'im, and their blood and limbs poured down into the valley below.
See also answer #1.
Targum Yonasan: Where they stopped because the inhabitants of Ar were not involved in the plot to kill Yisrael.