After Havdala one recites Vayiten Lecha. It is recited even on a Motzei Shabbos that Vayehi Noam is omitted such as when Yom Tov falls during that week. [Our custom is to say it together with another person, possibly in order so each one blesses the other. Some are particular to say it together from the same Siddur. Some say one is to recite Vayiten Lecha immediately after Havdala. The Rebbe Rashab however questioned this and he himself was accustomed to at times delay saying Vayiten Lecha after Havdala.]
Is Vayiten Lecha recited on Motzei Yom Tov?
Is Vayiten Lecha recited on Motzei Shabbos Chol Hamoed?
Is Vayiten Lecha recited on Motzei Shabbos which coincides with Yom Tov?
Is Vayiten Lecha recited on Motzei Shabbos which coincides with Tishe Beav?
May an Avel recite Vayiten Lecha?
If one did not recite Vayiten Lecha on Motzei Shabbos until when should it still be recited?
This matter requires further analysis.
Must one stand when reciting Vayiten Lecha?
 See Ashel Avraham Butchacher 298 for why we say it after Havdala as opposed to before. This was also the custom of the Arizal, as mentioned in next footnote.
Other Opinions: Some say Vayiten Lecha before Havdala. [Levush, brought in Biur Halacha 295 “Aval”]
 Siddur; Mentioned in 295/3; This was the custom of the Arizal [brought in Shaareiy Teshuvah; Kaf Hachaim 295/12; Shaar Hakolel 32/4] See Piskeiy Teshuvos 295/4 for a thorough analyses on this custom.
 So was the custom of the Rebbe Rayatz and other of our Raboseinu Nissieinu. [Shaareiy Halacha Uminhag 5/35]
 Shaareiy Halacha Uminhag ibid; Segulos Yisrael 80 likewise brings this custom in name of certain Tzadikim; Some say based on Zohar it is to be said in public. [See Piskeiy Teshuvos ibid]
 So is implied to also have been the custom of the Rebbe Rayatz as brought in Shaareiy Halacha Uminhag ibid
 The Chassid Rav Munya Munsazen in name of the Rebbe Mahrash of whom he says he heard it from his mouth. Some explain this can be inferred from the Siddur of Admur which states “after Havdala say Vayiten Lecha”.
 See Migdal Oaz story 174
 PM”G 295 M”Z 3; Beir Heiytiv 491/1
 Elya Raba 491/2; Aruch Hashulchan 295/3 His reasoning is because Chol Hamoed is forbidden in Melacha, and it is hence a belittling of Chol Hamoed to bless the weeks Melacha.
 Hayom Yom 19th Nissan
 PM”G 491 M”Z 1
As it is not respectful to bless the weeks Melacha on Yom Tov.
 Rama 559/2
 Peri Megadim 295 M”Z 3
 Gesher Hachaim 20/3-3 based on Rama 559/2; Rav SZ”A SSH”K 62 footnote 155
 The reason: Although this is certainly not required from the letter of the law, as all blessings may be said sitting other than the blessings of Asher Kidishanu, nevertheless seemingly the custom is to stand out of honor of the blessing, similar to the Kohanim who stand when they bless the Jewish people. Likewise the Rebbe would stand while reciting the Birchas Habanim on Erev Yom Kippur, and so is the widespread custom of Jewry. [Heard from Harav A.L. Hakohen; See 690/1 that the Megillah reader stands in honor of the congregation, but is not required to stand in private]
The Rebbe’s custom: The Rebbe’s personal custom was to to say Havdala at home and then sit and recite Al Hagafen and recite Vayiten Lecha by himelf while remaining in a sitting position. [Heard from Rav Chesed Halbershtam, the Rebbe’s Mashbak, who witnessed this every Shabbos for many years] He however also did not recite Vayiten Lecha with another person, and hence perhaps for this reason he did not stand.
 As this standing is not an obligation but a mere custom, and hence in any time of need one may certainly be lenient. [See Birkeiy Yosef 131/7-8; Biur Halacha 690 “Aval Lo Yikra”]