First we need to figure out if belief in Mosaic authorship is an ikar emuna (if it is, that would obviously mean that there is no room for it in observant Judaism, since it would be labeled as heresy). We also need to address the question if the study of biblical criticism threatens the authority of the Torah and its divine origin.
The main Chazalic sources
Now, the Mishna in Sanhedrin 90a states,
and these (listed below) don’t get a portion in the world to come:
one who says ‘there is resurrection of the dead according to the
Torah’; or ‘Torah is not divine etc.
This is the main source regarding the parameters of emuna and kefira/heresy. Though the Mishna only addresses the question as to “who gets oilam habu”, the Rambam assumes that this Mishna has some bearing on the question regarding “who is a heretic” as well. So far we haven’t seen anything about belief in Mosaic authorship of the Torah. The Mishna merely states that a Jew must believe in the divine origins of the Torah or that תורה מן" השמים". The Gemara in Sanhedrin (99b) writes regarding the words of the Mishna “Torah min hashmayim”,
for he scorned the word of god’ (Bamidbar 15:31), this refers to one
who says the Torah is not divine. Even if he says that the entire
Torah is divine besides for one verse which god did not speak, but
Moses said it on his own is included in the verse ‘for he scorned the
word of god.
Here too we don’t find any mention of Mosaic authorship being an ikar emuna, but the belief in the divine inspiration of the author/authors of the Torah.
The Rambam codifies this belief in his Mishna Torah and in his Perush hamishnayot (in the beginning of perek chelek), and makes the belief of “Torah min hashamyim”, an ikar. However he adds a few words (Hilchos Teshuva 3:8) that are not mentioned in the Gemara itself: “אם אמר משה”, “if Moses said it”. It is not clear if the Rambam is trying to say that the belief in Mosaic authorship is in itself an ikar (meaning that doubting this in itself constitutes heresy), or that the Rambam is merely giving an example of a prophet (Moses), saying that mere doubting that the transcriber of the Torah was a prophet constitutes heresy, since that would be the equivalent of denying the divinity of the Torah altogether. The words of the Rambam in Perush Hamishnayot are too ambiguous to infer from them anything regarding Mosaic authorship, but we can deduce from his ikrei emunah how he would have viewed the evolutionary aspect of the documentary hypothesis as we will see now.
The Rambam in his 8th ikar emuna writes that a Jew must believe that the way Tefillin and Succah is done by Jews today is the same way it was done in the days of Moses. Since the documentary hypothesis posits that the Torah and Halacha has evolved, it would clearly constitute heresy according to the Rambam. However since the ikar is not mentioned in the Mishna or Talmud, the defender of biblical criticism (in accordance with Jewish law) may argue that it still fits the scope of "תורה מן השמים", as he agrees that Chazal interpreted the Torah through divine inspiration, and may come to regard the above ikar an invention of the Rambam himself. On the other hand, we must admit that the documentary hypothesis would most probably constitute heresy according to the Rambam.
The orthodox minimalist view
The first affirmation of the orthodox minimalist view that "Mosaic authorship of the Torah" is an ikar emuna is found in the Ani Maamin (article number 8), “I believe with perfect faith that the entire Torah presently in our possession is the one given to Moses." This is a clear declaration that a Jew must believe that the Torah was written by Moses himself, and that it wasn't tampered by anyone else besides for Moses. According to this position, one who doesn’t accept the Mosaic authorship of the Torah is a heretic. However, as we have already seen this does not necessarily reflect the view of Chazal or the Rambam, in their words the only belief required of the Jew is that he believe that the Torah is of divine origin. That Mosaic authorship is an ikar emuna (not merely a Jewish tradition) is an invention of the author of Ani Maamin. See also Tiferes Yisroel beginning of perek chelek ois vav, he seems to agree with the author of the Ani Maamin that Mosaic authorship is an ikar. See also Shut R’ Moshe, YD 3 vol. 6, siman 114-116. From these teshuvos It is evident that he accepts Mosaic authorship for an ikar, though he doesn’t feel the need to defend this position as it is self-evident to him.
The maximalist view: Ibn ezra and other chazalic sources
Now the Ibn Ezra (the Tzafenat Panaeach also cites him in the end of Parshat Vayishlach) in a few places in his commentary hints that the Torah might have been edited by different people, and that certain words were added only after the Israelites conquered the land (see his commentary on Dvarim 1:2). See also the Tziyuni al haTorah Bamidbar 21:17. This supports the position that belief in Mosaic authorship is not an ikar emuna, and that dismissal of it is not heresy (unless we say that the Ibn Ezra himself was a heretic). The Tzafenat Panaeach also writes clearly that Mosaic authorship is not an ikar emunah
And since we must believe in the words of tradition and prophecy, what
difference does it make whether Moses or some other prophet wrote it,
since the words of all of them are truth and given through prophecy.
There is also evidence from the Midrashic literature that the Torah was edited by other scribes. In a few places (see for example Rashi Breishis 18:22) the Rabbis point out that it would have been more appropriate for the Torah to write in different way, only that the scribes (Ezra and his assembly) edited it when they felt the need to. “ תיקון סופרים הוא זה". From these and other similar statememts we see that the Rabbis themselves were comfortable with the idea that the Torah was edited by different people other than Moses, although they surely believed that they all did so with divine inspiration. This lends credence to the idea that Mosaic authorship was never intended to be an ikar emunah, as the Rabbis themselves questioned this tradition. A similar tradition is found in Bamidbar rabbah (III, 13) in the name of yesh omrim that the Eser nekudot signify that they were added by Ezra himself,
If Elijah comes and asks: "why have you written these words?" I [Ezra] Shall
answer: "That is why i dotted these words".
See also Rashi Dvarim 34:5 regarding the last eight verses of the Torah.
(Note: nowhere does the Torah claim that it was written in its entirety by Moses . The Torah only states in a few places that the previous Parsha was written by Moses, but that never includes the whole book. After Parshas Mishpatim (Shmos 24:4) the Torah makes such a statement. And the same claim we find by the Maso’es of the Israelites (Bamidbar 33:2). The only book that is claimed to be written (almost) in its entirety by Moses is sefer Devarim (31:9). [Indeed this is the only sefer that’s called “Toras Moshe” in the Tanach. See Joshua 8:32; 2 Melachim 14:6]. And even that doesn’t preclude small edits by other scribes).
Resolving the issues
Although we haven’t seen anything yet close to the study of biblical criticism or the belief in the documentary hypothesis (saying that small edits cropped in the text is wholly different than saying that different portions were written by different authors and only compiled much later) some modern Rabbis stretch this argument and say: since we haven’t seen anything conclusive yet in the Gemara or in the Poskim regarding the belief in Mosaic authorship, and we do find some Rabbinic literature (and Rishonic literature as well) supporting the idea that Mosaic authorship in the traditional sense is not an ikar, there is no reason for us to draw the line and stop here, for this would be an arbitrary distinction; for the same price we may as well endorse the documentary hypothesis.
One might still argue and say, if we acknowledge the scholarly position that portions of the Torah were written by different authors, when they often contradict each other, then we are essentially denying the divinity of the Torah, since Hashem surely does not utter contradictions! This problem can easily be resolved through the Gemara in Eiruvin 13b, “three years the Bais Shammai and Bais Hillel argued, one would say the Halacha is like us and one would say the Halacha is like us, a heavenly voice came out and announced: both [schools] are the words of god, but the Halacha is like Bais Hillel etc.” The concept of "אלו ואלו דברי אלהים חיים" states that even two contradictory opinions can be true in the sense of them both being divinely inspired. In a similar vein, all of the different contradictory verses evident in the Torah can be said to be divinely inspired, as every author tries to derive new laws from the broad principles set forth by Moses which are the words of god. In light of this we can even say that all 613 Mitzvos are of Mosaic origin, though he didn’t command us to do all of them, all of the Mitzvos can be attributed to him since the authors of the Torah all derive their laws from his words. This theory is advanced by Jacob Milgrom in the introduction to his book Leviticus (a book of ritual and ethics) where he shows that even critical scholarship can believe in the Mosaic origin of the Mitzvos.
This theory works for the biblical narratives as well; although we admit that they were composed by different authors each advancing his own position and writing a different version of the biblical traditions, they were all equally inspired by god to speak and write and enlighten the Jewish nation. Here, the conservative might argue that if we admit that there are different versions (of narratives) in the Torah, then we are essentially saying that some parts of the Torah are not true, since when we’re dealing with contradictory versions, obviously, only one can be true. However, one can still argue that the minimum requirement is that the Jew believes in the divine origin of the Torah, since it is sensible to believe in the documentary hypothesis and at the same time believe that the authors were divinely inspired (as we have proven from the Gemara in Eruvin), this would suffice for the belief in “תורה מן השמים”.
If one accepts biblical criticism he must reject the notion that the words of the Torah were dictated by god to a person, since god cannot dictate contradictory laws and verses to different people. He must say that the Torah is heavenly in the sense that it has been divinely inspired by its authors similar to the inspiration of the sages of the Mishna and Talmud. However this does not deter some modern orthodox Rabbis to embrace such a belief, since nowhere is it mentioned that divine dictation is an ikar emuna. The position that biblical criticism and Jewish orthodox belief system are compatible is advanced by a few modern orthodox Jewish Rabbis including: Rabbi Louis Jacobs in his book “we have reason to believe”; Abraham Joshua Heschel professor at the JTS; David Weiss Halivni; Rabbi Jeremy Rosen.
Though mainstream orthodoxy does not allow for any other biblical authors besides for Moses and advances the minimalist position, regarding the Mosaic authorship of the Torah, and considers this belief to be an ikar emuna, some Rishonim allow for some edits to have been added after Moses’s death by divinely inspired scribes. Since biblical criticism is a relatively new study we cannot know if the Rishonim and Rabbis would have endorsed such a radical view as the documentary hypothesis. However, since Mosaic authorship is not mentioned in the Gemara or the Rambam to be an ikar emuna (unequivocally), some modern orthodox Rabbis embrace biblical criticism and take the maximalist position regarding the definition of "תורה מן השמים".
 Literally it translates as “Torah is not from heaven”.  A composition that is based on the Rambam’s ikarim, but was not composed by the Rambam himself, and has some significant differences with the Rambam’s original ikarim enumerated in his Perush hamishnayot. The author of the Ani Maamin is unknown.  Rabbi Mordechai Breuer in his debate with Professor Israel Knohl remarked, “I do not know if [ibn Ezra’s] words were to the liking of the rabbis. In any event, they were uttered by Ibn Ezra, and we can therefore not reject their legitimacy.”  However, see Tiferes Yisroel for different interpretation. Almost all the meforshim explain it similarly. But of course my interpretation of the Midrash is more straightforward. See also Dr. Marc Shapiro in "Maimonides' Thirteen Principles: The Last Word in Jewish Theology?". His words have been quoted by mevaqesh in his answer. See also Abarbenel's introduction to Jeremiah regarding the meaning of keri and ketiv. JPS Torah commentary Numbers by Jacob Milgrom pp. 375-376 that according to one medieval tradition the verses in bamidbar (10:35-36) were excerpted from a source known as "The prophecy of Eldad and Medad". This idea may be alluded to by R' Yehuda Hanasi when he says "[They are marked] to indicate that they form a separate book" (sifri bamidbar 84).
 However see Ramban Devarim 31:9. But this is not the only way to read the verse. The simple interpretation is that it refers to sefer Devarim only.  However see Tzafenat Panaeach end of Vayishlach. He writes that the Ibn Ezra himself did not endorse large scale criticism as is evident from his commentary to Breishis 36:31.  http://www.jpost.com/Jewish-World/Judaism/We-Have-Reason-to-Believe  in his books "revelation restored" and "Peshat and "Derash".  http://thetorah.com/torah-misinai-and-biblical-criticism/ see also http://thetorah.com/in-what-sense-did-orthodoxy-believe-the-torah-to-be-divine/.