I would like to know if it is permitted during these times to recite Tehillim at night for the sake of all of the ill injured and captured citizens and soldiers?
Those who are accustomed to not recite Tehillim during nighttime, and so is the Chabad custom, are likewise not to recite Tehillim even during times of war and the like, until midnight. Rather, the Tehillim is to be scheduled to be recited during daytime or after midnight. However, if the matter is urgent for that moment, such as a military attack is taking place at that very moment, a sick person is entering into surgery at that moment, or a birth is taking place at that moment, which happens to be at night, then many Poskim are lenient and indeed the widespread custom is to permit saying Tehillim at night in such a case. Nonetheless, some Poskim and communities are stringent even in such a case. There is no clear Chabad directive in this matter other than the general widespread custom to be lenient.
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. Based on this, many Poskim rule that one is not to read verses of Mikra [Written Torah] at night.
Now, it is debated amongst the Poskim as to the degree of the general restriction against reading the written Torah during nighttime, and as to whether it also applies to the recital of Tehillim. Amongst the reasons for being stringent is because Mikra is in the world of Assiya and the nighttime is also Assiya, which is judgment, and one is thus not to arouse judgment at night through learning Mikra and doing so is a Sakana, and hence perhaps one should not read Tehillim at night even for the sake of the sick. However, some are accustomed to be lenient regarding the recital of Tehillim, especially if it is being read at night for the sake of the sick, as David asked Hashem to consider the recital of Tehillim to be similar to the learning of Negaaim.
Practically, the Chabad custom is to be stringent both regarding the written Torah and Tehillim to not recite it at night starting from nightfall until midnight. However, even amongst those who are generally stringent against reading to Tehillim at night [i.e. Chabad] many Poskim are lenient to permit its recital for the sake of an urgent matter, and so is the custom of many to recite Tehillim during labor even if it occurs at night prior to midnight. Nonetheless, some Poskim are stringent even in such a case.
Sources: See regarding the restriction against reading Mikra at night: May not do so: 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 Beir Heiytiv; May do so: Shaar Hatziyon 238:1 based on Peri Megadim 238 A”A 1 who 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 permitted from the letter of the law See regarding if this applies also against reading Tehillim: Yes, don’t read Tehillim at night: Chaim Sheal 25; Likkutei Maharich; Maharsham 1:158 in name of Zechor Leavraham and Yosef Ometz; Ben Ish Chaiy Pekudei 7; Rav Poalim 2:2; Kaf Hachaim 238:9;Yitzchak Yiranein 1; Sefer Haminhagim p. 41 [English]; Igros Kodesh 18:31 [printed in Shulchan Menachem 1:374]; Toras Menachem 48:122; Toras Menachem 1985 5:3103 No, may read Tehillim at night: Kikar Laeden 5:7 [Chida], Mentioned in Igros Kodesh ibid; Ashel Avraham Butchach 238; Na’ah Lehodos on Tehillim 119 and Shemo Yitzchak; Divrei Yatziv Y.D. 136:2; Kumi Runi p. 20; Meateh Tehila see also Siddur Yaavetz; Levushei Mordechai Tinyana 186; Betzeil Hachochma 4:46; Pamei Yaakov 69:104 [Rav Ovadyah Yosef] in name of many Sefarim; Piskeiy Teshuvos 238 footnote 24 See regarding reading Tehillim after midnight: 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; Sefer Haminhagim p. 20; Igros Kodesh 18:31 [printed in Shulchan Menachem 1:374]; Toras Menachem 1985 5:3103; Rebbe in Toras Menachem 48:122; Rebbe in Sichos Kodesh 5734 2 p. 435, printed in Toras Menachem 4 p. 124 See regarding reading Tehillim at night for an urgent matter: No, even when urgent don’t read: Rav Poalim 2:2; Or Letziyon 2:46; Tehillim Igara Dehilula; Adir Bamarom 387; Zechor Leavraham 62; Tiferes Banim on Kitzur SHU”A 1:5; Sefer Zichron Beis Kelm p. 28Yitzchak Yiranein 1 Yes, may read when urgent: Vayechi Yaakov O.C. 9; Os Habris on Tehillim; Likkutei Maharich 1 Tikkun Chatzos; Meiy Yehuda Altman 22; Tzitz Eliezer 8:2; Beir Moshe 4:22; Pamei Yaakov 69:104 [Rav Ovadyah Yosef] in name of many Sefarim; Yabia Omer 6:30; Yalkut Yosef Bikur Cholim p. 57 in name of Chida in Avodas Hakodesh, Yaskil Avdi, Betzeil Hachochma 4:45; This follows the ruling of the Ashel Avraham of Butchach ibid who states Tehillim may be recited at night being it is a prayer and not learning.