Learning and reading Tanach at night Chumash/Navi/Tehillim]:
A. The avoidance:
Many Poskim rule based on Kabballa that one is not to read verses of Mikra [Written Torah] at night. This includes verses from Torah, Neviim, Kesuvim, as well as the recital of Tehillim. It includes even the recital of only part of a verse. It is for this reason that some are accustomed not to recite psalms during the Maariv night prayer. Other Poskim however rule it is permitted to read Mikra at night, although it is better to do so during the day. Other Poskim rule that while Mikra may not be read at night, one may recite Tehillim. Practically, one is to be stringent in this matter not to read any Mikra at night, including Tehillim and so is the Chabad custom. However there are people those that are accustomed to be lenient.
Studying together with a commentary: One may study Mikra together with a commentary at night. Thus, if one did not complete the daily Chumash before nighttime he may study Chumash at night together with Rashi.
Studying in a different language: One may read and study Mikra at night in a language that is not Hebrew.
May one who does not know any Torah Shebaal Peh, read Torah Shebechsav at night?
One is not to read Shnayim Mikra at night with exception to Friday night in which case it may be read. Regarding Thursday night see footnote. One may read Shnayim Mikra at night if he reads it together with a commentary such as Rashi. Nevertheless, even in such a case he is not to read Targum at night.
B. When the avoidance applies:
From what time at night does the above adherence begin? The above avoidance of reading Mikra begins from nightfall. However, prior to nightfall, one may read Mikra even if it is after sunset. Thus, the daily Tehillim may be recited after sunset, up until nightfall.
Until what time at night does the above adherence apply? Some Poskim rule that one is not to read Mikra, including Tehillim, even after midnight, until daybreak. Other Poskim rule that while Mikra is not to be read until daybreak, Tehillim may be recited after midnight. Other Poskim rule that all Mikra may be read after midnight. Practically, one may read Tehillim after midnight, however not Tanach.
Days in which one may recite Tehillim at night:
May one recite Tehillim/Mikra on Friday night and the night of Yom Tov?
Yes. It is permitted to recite Tehillim on Friday night.
May one recite Mikra on Thursday night?
Yes. It is permitted to read Mikra on Thursday night. Accordingly, it is permitted to recite Tehillim on Thursday night.
May one recite Mikra on the night of Rosh Chodesh?
 Rikanti Yisro; Arizal in Shaar Hamitzvos Vaeschanan, brought in Birkeiy Yosef 238/2; Chaim Sheal 25; Beir Heiytiv 238/2; Siddur Yaavetz; Ben Ish Chaiy Pekudei 7; Yesod Veshoresh Haavoda 6/2; Or Hachaim Haazinu; Likkutei Maharich Seder Kevius Itim Latorah; brought in Shaar Hatziyon 238/1 in name of Beri Heiytiv
 The reason: The Midrash [Tanchuma Ki Sisa 36; Pirkei Derebbe Eliezer 46] states that Moshe Rabbeinu did not experience day and night during his 40 day visit in heaven, after the giving of the Torah on Har Sinai. How then did he know when it was day? This he would know through when Hashem teaching him the written Torah. When he was taught the written Torah he knew it was day and when he was taught the oral Torah he knew it was night. [Birkeiy Yosef ibid; Or Hachaim ibid; Likkutei Maharich ibid; Shaar Hatziyon ibid; See also Tana Divei Eliyahu 2] Alternatively, the reason is because Mikra is in the world of Assiya and the nighttime is also Assiya, which is judgment, and one is this not to arouse judgment at night through learning Mikra. [Arizal ibid brought in Ben Ish Chaiy ibid; Kaf Hachaim 237/9] Doing so is a Sakana. [Yesod Veshoresh Haavoda] However Torah Shebaal Peh is Chesed, and hence helps neutralize the judgment of night. [Avnei Tzedek Seagate, brought in Likkutei Maharich ibid]
 Chaim Sheal 25
 Yesod Veshoresh Haavoda ibid
 For example: The Sefaradim are accustomed to say Barchi Nafshi prior to Maariv on the night of Rosh Chodesh. Some Sefaradim are accustomed not to recite it due to the above reason.
 Shaar Hatziyon 238/1 based on Peri Megadim 238 A”A 1 which states one is to learn Mikra, Mishneh, and Talmud also at night. [Shaar Hatziyon ibid] Nevertheless he concludes that it is best to read it during the day; Maharsham 1/158 that it is eprmitetd from the letter of the law
 Ashel Avraham Butchach 238
 The reason: As David asked Hashem to consider the recital of Tehillim to be similar to the learning of Negaaim. Hence we see that it is similar to the oral Torah. [Ashel Avraham ibid]
 Sefer Haminhagim p. 41 [English]; Igros Kodesh 18/31 [printed in Shulchan Menachem 1/374]; Toras Menachem 48/122; Toras Menachem 1985 5/3103
 Kikar Laeden 5/7 [Chida]; Mentioned in Igros Kodesh ibid; see also Siddur Yaavetz; Levushei Mordechai Tinyana 186; Piskeiy Teshuvos 238 footnote 24
 Yesod Veshoresh Haavoda ibid; Vayechi Yaakov 9; Avnei Tzedek Seagate, brought in Likkutei Maharich ibid; Sefer Haminhagim p. 20; Igros Kodesh 18/31 [printed in Shulchan Menachem 1/374]; Toras Menachem 48/122; see Ben Ish Chaiy Pekudei 7
The reason: As when studied with a commentary one can consider it as studying the Oral Torah. [Rebbe ibid]
 Ben Ish Chaiy Pekudei 7
 Chida in Pesach Eiynayim, brought in Ben Ish Chaiy Pekudei 7
 Beis Yisrael brought in Piskeiy Teshuvos 238/12
 Likkutei Mahrich ibid in name of Zechor Leavraham 1 Mareches Taf in name of Rameh
 Beir Heiytiv 238/2 states in name of Arizal that one is not to learn Tanach at night. This ruling is quoted by many Poskim. So also rules the Rebbe as is evident from Shaareiy Halacha Uminhag 1/24;
Regarding Shnayim Mikra: So is ruled explicitly in Lekutei Mahrich [Seder Kevius Itim Letorah] that Shnayim Mikra is not to be said at night.
Other Poskim: Shaareiy Tziyon 238/1 rules one may read Mikra at night, however it is better to do so during the day.
Regarding if one may read Mikra after midnight: No. This allowance only applies to Tehillim. [Kaf Hachayim 237/9; Ben Ish Chaiy Pekudeiy 7; Lekutei Mahrich ibid; Shaareiy Halacha Uminhag ibid]
 Ben Ish Chaiy Pekudeiy 7; Kaf Hachayim 237/9
 Some opinions allow reading Mikra on Thursday nights. [Or Tzadikim; Mishnas Chassidim; Siddur Rav Shabsi; Yesod Veshoresh Haavoda; Ben Ish Chaiy Pekudei 7 “One may read 26 Pesukim”] Others go even further to state it is customary to recite Shnayim Mikra specifically on Thursday night. [Machazikei Bracha in name of Rashash] Nevertheless, some rule this allowance applies only to Mikra and not Targum. [Machazikei Bracha in name of Rashash brought in Likkutei Mahrich ibid] To note however from the custom of the Chabad Rabbeim [Hayom Yom 4th Teves] to read the first and at times also the second portion of the Parsha on Thursday night. It is implied there from the wording [Maavir Sedra] that they also read Targum.
 Yesod Veshoresh Havodah Shaar Hanitzutz chapter 2; Shaareiy Halacha Uminhag ibid
 Likkutei Mahrich ibid in name of Zechor Leavraham 1 Mareches Taf in name of Rameh
 Igros Kodesh 18/31 [printed in Shulchan Menachem 1/374]; Sefer Haminhagim p. 41 [English]; Mi Yehuda 22; Piskeiy Teshuvos 238/3
 Chaim Sheol 25 ibid based on Arizal and Rav Shalom Sharabi and that so is the custom of the Mekuballim; Likkutei Maharich ibid; Maharsham 1/158 in name of Zechor Leavraham and Yosef Ometz
 Ben Ish Chaiy Pekudei 7 in name of Chida who heard so from an Adam Gadol; Custom of many as brought in Chaim Sheol ibid; Kaf Hachaim 238/9
 Or Tzaddikim, brought in Likkutei Maharich ibid
 Kaf Hachaim 238/9 that so is the custom; Sefer Haminhagim p. 20; Igros Kodesh 18/31 [printed in Shulchan Menachem 1/374]; Toras Menachem 1985 5/3103
 Sefer Haminhagim p. 41 [English]
 Yosef Ometz 54; Or Li [of Sdei Chemed] 40; Rav Poalim 2/2; Ben Ish Chaiy Pekudei 7; Kaf Hachaim 237/9; Yesod Veshoresh Haavoda 6/2; Maharsham 1/158
Chabad Custom: See Sefer Haminhagim p. 41 [English] that does not list Shabbos and Yom Tov as one of the days that permit Tehillim to be said at night. This implies that one is not to read Tehillim/Mikra even on Friday night. See also Toras Menachem 48/122 which does not mention Friday night. However it was witnessed that the Rebbe said Shnayim Mikra on Friday night. [See Hiskashrus ]
 Shaar Hamitzvos Vaeschanan p. 34; Likkutei Maharich ibid in name of Or Tzadikim; Mishnas Chassidim; Siddur Rav Shabsi; Yesod Veshoresh Haavoda; Ben Ish Chaiy Pekudei 7 “One may read 26 Pesukim”; The custom of the Chabad Rabbeim is to read the first and at times also the second portion of the Parsha on Thursday night. [Hayom Yom 4th Teves]
 Divrei Yatziv Y.D. 136
 Rav Poalim 2/2; Ben Ish Chaiy Pekudei 7; Kaf Hachaim 237/9