The Molad of this past month of Adar was on Sunday, the 30th of Shevat at 6:20 AM. Accordingly, this past Motzei Shabbos was not yet seven complete days past the Molad and the question is asked regarding if one may have recited Kiddush Levana last night.
Must one wait seven complete days [i.e. Zayin Shleimim] from the Molad to say Kiddush Levana?
Some Poskim rule it is not necessary to wait until seven full days pass from the Molad, and rather as soon as six days have passed and one has now entered into the seventh day past the Molad, Kiddush Levana may be recited. Others however rule that based on Kabala one is to wait for a full seven days to pass from the Molad before saying Kiddush Levana. Practically, one may be lenient in this matter.
Moshe Rabbeinu was born and passed away on Zayin Adar. One is to increase in joy on this day. Some are accustomed to fast. This is not the Chabad custom. However one should increase in charity on this day in exchange for the fast. Some do not say Tachanun on this day.
 Rameh Mepuno 78; Shiyurei Kneses Hagedola; Elya Raba 426/14 [brought in Shaareiy Teshuvah 426/10] that one may say Kiddush Levana on the night of the 7th; Ashel Avraham Butchach 426/2
 Birkeiy Yosef 426/4 brought in Shaareiy Teshuvah 426/10; Mateh Efraim 581/10 rules one is to initially say it only after seven complete days have passed, although if he suspects the moon will not be visible again, he is not to delay the blessing.
 So concludes Hiskashrus 454 p. 15 and so was the custom of Rav Yaakov Landau [as told to me by his son Rav Eliyahu Landa Shlita].
Seemingly the reason one may be lenient is because even regarding waiting seven days there is a dispute and the Rebbe leaves room to be lenient. See also Sichas 1986 6th Adar Rishon that Kiddush Levana was said that Motzei Shabbos even though seven full days had not passed since the Molad.
 Gemara Sota 12b
Was Moshe born during a leap year? The Gemara records a dispute on this matter: Some say Moshe was born on Adar Rishon of a leap year. Others say he was born in a regular year with a single Adar. [ibid]
On which weekday, and at what time, did Moshe pass away? Moshe passed away on Shabbos afternoon, towards the time of Mincha. [Admur 292/5]
Did Moshe pass away during a leap year? The M”A 580/20 brings a dispute on this matter. The Terumos Hadeshen 294 writes Moshe passed away in a regular year that contained one Adar. However the Yalkut Yehoshua writes that there are opinions who say Mosher Rabbeinu passed away during the first Adar of a leap Year. According to the opinion in the Gemara that Moshe Rabbeinu was born on Adar Rishon one must conclude that he also passed away on Adar Rishon, as it states regarding Moshe that Hashem filled his years that he lived an exact amount of years. [Sheilas Yaavetz 1/117; Likkutei Sichos 16 p. 344 footnote 40]
Other Opinions: Some opinions say that Moshe passed away on the 7th of Shevat. [brought in M”A 580/20] The Midrash states that Moshe was born and passed away on the first of Adar. [Esther Raba 16] However the Anaf Yosef attributes this to a misprint and it should read the 7th of Adar, as stated in the Talmud.
 Hisvadyos 1988 2 p. 388 [printed in Shaar Hamoadim Adar 17] The Rebbe there states as follows: It is found that Chassidim do not mark this day with any special event. This is puzzling. Hence one is to mark it with increase in joy as is befitting of the Yom Hahilula of a Tzaddik, and especially Moshe Rabbeinu. Likewise, it is also his birthday, thus giving a double reason to celebrate. [ibid] On another occasion the Rebbe stated that it should have been proper to establish the joy of this day similar to the celebration that is accustomed on Lag Baomer. [Sichas listed in Otzer Minhagei Chabad 28]
 Michaber 580/2
 As Chassidim are accustomed to not increase in fast days. [Rebbe in Shaar Hamoadim ibid; Sichas listed in Otzer Minhagei Chabad 28]
 Rebbe ibid
 The Chabad Rabbeim did not say Tachanun on Zayin Adar starting from the Mincha of Vav Adar. Nevertheless, this custom only began once they took leadership of the movement and not beforehand. [Sefer Haminhagim [English] p. 168]
The reason: As the soul of Moshe shines within the leader of each generation, and hence they feel the value of the birth of Moshe on this day. [Likkutei Sichos 16 p. 350-351]