Why does the Torah confer the title of 'Navi' upon a Navi Sheker?
Ramban #1: It is not the Torah that calls him a Navi but the Navi Sheker himself.
Ramban #2: The ability to foretell the future is something that some people have in their genes. 1
If one may not listen to a Navi Sheker, who declares a false prophecy, why does the Torah need to add "Cholem Chalom, whose level of prophecy is lower than that of a Navi?
Oznayim la'Torah: To teach us that even the Cholem Chalom, who dreamt be'Oneis - as apposed to the Navi Sheker, who prophesied intentionally - is Chayav Misah, not for his dream, but for verbalising it. 1
Oznayim la'Torah: Which he obviously did in order to lead the people astray.
What is the difference between an "Os" and a "Mofeis"?
Ramban #1: "Os" 4 is when a Navi predicts that something will happen that proves a certain point; 5 whereas "Mofeis" is a supernatural occurrence. 6
Ramban #2 (citing the Sifri): There is no difference between Osos and Mofsim, and they are one and the same. 7
Rashi: As in Shoftim, 6, 39.
Rashi: As in Bereishis, 1:14.
Ramban: From the root "Asah", in Ha'azinu, 33:2.
Ramban: As in Yeshayah, 7:14.
Ramban: As in Divrei Hayamim 2, 32:31 and in Yo'el, 3:3. See Ramban DH 've'Nasan Eilecha' who elaborates at length on the Osos and Mofsim that took place in Egypt.
See Ramban.
Why does Hakadosh-Baruch-Hu empower Resha'im to perform miracles?
Rashi (citing R. Yossi ha'Gelili in Sanhedrin, 90a) and Rashbam: To test us. 1
Ramban: Refer to 13:2:1:2*.
Hadar Zekenim and Rosh (in Pasuk 3, both citing R. Akiva in Sanhedrin 90a): The Torah is actually referring to a genuine Navi - such as Chananyah ben Eizor - who performed Osos and Mofsim, and who strayed afterwards from the path and] told the people to serve idolatry; and the Torah is warning us not to rely on him, even though he previously performed miracles. 2
Rashi: As the Torah specifically writes in Pasuk 4. Rashbam: The Os and Mofeis refer to miracles that the Navi Sheker performs by predicting the future, which he achieves via the powers of Tum'ah - Terafim, Ov or Yid'oni - and which Hashem grants him the power to master in order to test us.
Rosh: And Hashem gives prophecy to someone who will later turn into a false Navi, in order to test us. All the more so should we not heed Nevi'im who performed [miracles] from the outset through witchcraft! See also Torah Temimah, note 3.
What sort of prophecy is the Pasuk referring to?
Ramban: It is referring to a prophecy that permits Avodah-Zarah even for one day, or that permanently negates any other Isur - such as eating Chazir or incest. 1
Ramban: But if he comes to permit an Isur on a one time basis - such as Eliyahu on Har ha'Carmel - who permitted offering on a Bamah at a time when Bamos were forbidden, then if he is an established Navi or he performs an Os or a Mofeis, we are obligated to listen to him - See Ramban DH 've'Hineh', who elaborates further.
In whose name is the Navi Sheker prophesying?
Ramban #1: He is prophesying in the name of the Avodah-Zarah that he wants us to worship. 1
Ramban #2 (citing Sanhedrin, 90a) and Seforno (on Pasuk 6): He is prophesying in the name of Hashem to worship a certain god. 2
Ramban: 'The image Pe'or who is god sent me to you, with the command that you worship him in such and such a way!' - See 18:20.
Ramban: 'Hashem ha'Nichbad sent me with instructions that you should worship Pe'or, who was My partner in the creation of the world!' or ' ... who is greater than all other deities before Him, and He wants you to worship him!'