Dear Rabbi, I downloaded a Zmanim app called "Simple Luach". On it there is an option in the settings to Use Tzeis HaKochavim 6.3 grades". This puts Tzeis HaKochavim exactly the same as Chabads but puts Havdalah only 4-5 minutes after Tzeis HaKochavim whereas Chabad Havdalah is typically 12 minutes after Tzeis HaKochavim. What is 6.3 grades and is it halachically reliable? The second part of my question is concerning davening. Can one daven Maariv before the allotted time for Havdalah on Chabad.org? I think the general practice in Chabad circles is to daven Maariv at the Havdalah time. Does a person have what to rely on in davening Maariv shortly after Tzeis Hakochavim or even before? I know part of Havdalah is in Shimoni Esri. Can one daven Maariv before Tzeis Hakochavim up till shimoni eseri and continue after towards the end of Shabbos?

ב"ה Shalom I will first quote from our own website in regard to calculation of Zmanim. "The subject of times is a very complicated one in Halacha, there are few rabbis who are experts on the subject, and are familiar with both all Halachic opinions and various astronomic calculations by which the times are determined." In your question you are adding the component of the Chabbad custom and the interpretation of the Ba'al Hatanya on these issues. If you follow the Chabbad Custom I can only advise you to consult your own Chabbad Rabbi how to conduct yourself, especially since I have read that there are various opinions in Chabbad in regard to the calculations of Shkiah and Tzet Hakokchavim. In regard to davening Ma'ariv on motzei Shabbat, though a person should not Daven Ma'ariv early , technically if a person is a situation in which one is forced to Daven Ma'ariv before Tzet Hakokcavim, (such as one has an important Mitzva to tend to) according to the Shulchan Aruch 293:3, one may do so and even make Havdala but without a candle of course. Obviously, in such a case this person , although he Davened Ma'ariv,one may still not do any Melacha until Shabbat is really out and must also repeat Kriat shema on time. All the best