Why would Edom be interested in the fact that Hashem listened to their cries?
Rashi: Moshe was referring to Yitzchak's B'rachah "ha'Kol Kol Ya'akov", which had come true (in which case "ha'Yadayim Yedei Eisav" was no longer applicable - Oznayim la'Torah). 1
We can add that Yitzchak specifically said "ha'Kol Kol Ya'akov" (Chaser 'Vav') implying "ha'Kal Kol Ya'akov" the B'rachah of "ha'Yadayim Yedei Eisav" can only take effect when "Kol Ya'akov" is weak - and here they were telling Edom that they Davened and their prayers were answered in which case they held the upperhand.
Who was the Mal'ach referred to in the Pasuk?
Rashi: The Mal'ach was Moshe 1 .
Targum Yonasan: The Mal'ach was one of the Mal'achei ha'Shareis.
And Moshe 'boasted' to the king of Edom and referred to himself as a Malach, in order to frighten him into submission. See Oznayim la'Torah. Rashi: This is also a proof that the Nevi'im are called 'Mal'achim' - as we find in Divrei ha'Yamim 2, 36:16. Though it is not clear how Chazal know that the title 'Mal'ach' is not confined to Moshe exclusively who was superior to all other Nevi'im.
Where exactly was Kadeish?
Rashi (in Yehoshu'a, 1:4): It was in Midbar Kadeish, alias Midbar Tzin, on the south-eastern tip of Edom. 1
Rashi (Ibid.): From which point they were destined to enter Eretz Cana'an.
