tiawd –
As I stated in my posts above, there are plenty of additional sources for the idea of the Tanya from sources not known to be affiliated with Lubavitch.
There is the statement quoted by many in the name of the Zohar ; מאן דנפח מדיליה נפח.
The Nefesh Hachaim in שער א פרק ה and פרק טו explains the Neshama pretty close if not the same as the Tanya.
I remember Rav avigdor Miller as well using the idea of Chelek Eloka Momaal to explain the words of the Chovos Halevavos who says in his Hakdama that והשכל הניצל מכל פגע is one of the three possible sources for dinim that are דאורייתא! The Gemara says למה לי קרא סברא הוא and Rav Miller’s explanation is this idea of the Chovos Halevavos that as Chelek Eloka Mimaal the סברא of an “undamaged mind” has the status of דאורייתא!
Your statement above “It is much more dangerous to blur the line between G-d and man than to over-emphasize the gap between us and Hashem, even if that is also a mistake.” is a fatal error and quite the contrary is the case.
It is the idea of Chelek Eloka Mimaal that has the power to inspire people (who view themselves and others as Chelek Eloka Mimaal) to emulate Hashem and seek to bestow kindness on others like Avaraham Avinu, to “over-emphasize the gap between us and Hashem” especially when it is “a mistake” as you suggest, is what leads people to lose all sense of humanity and sink to the level of animals in their own behavior and especially in their behavior towards others.
I don’t think anyone has ever gone off the derech by getting “carried away” with the idea of Chelek Eloka Mimaal (aside for Pharaoh and a few others) while an unfortunate amount of people have sunk to unthinkable levels of inhumanity due to the idea being neglected.
Philosophically the “fallacy” and “absurdity” (as well put by Yechi above) of your questions are well exposed in my posts above, after a basic understanding of אין עוד מלבדו, as explained by others in addition to the Tanya, you’re questions are all what is known in the Beis Medrash as a “Klotz Kasha”.
Your questions are like a question I once heard from a Lomdishe rebbe of mine who asked, why is it muttar to daven while wearing Tefillin if it is assur to be מסיח דעת from ones Tefiliin?
I will leave off with one more question for you, it says שמע ישראל ה’ אלו’ ה’ אחד how can there be Hashem and Elokim if “G-d cannot be divided into parts.”??