Verse 1-2: Krishna starts with a metaphor -A tree with the roots on the top and branches at the bottom is known as imperishable.  Ved are the leaves on the branches.  The tree extends up and down and the sprouts represent the three modes of nature (sat, raj, tamas).  The branches grow upwards and downwards.  The three modes of nature give rise to sense of self.  Even the roots (Consciousness) gets entangled in the action and its consequences in this human world.  I am not sure what is the reference here to the inverted tree, however, the commentators seem to link it to the description that Universal Consciousness is the source of everything (roots up top) and the branches are the material manifestation.  Knowledge about right or wrong is in Vedas.  To me it appears more metaphorical, in terms of saying that the root of everything is Universal Consciousness which is above all (not physically on top) and all else is manifestation which is lower than the Ultimate Consciousness (not physically below the root).  

Verse 3-4: This inverted tree is not visible from any part of the tree, as the consciousness is entangled in material attachments.  With the weapon of detachment one can finally see the truth and get liberated.

Verse 5-6:  Once the self is detached it gives up the illusion and ego.  It becomes free from lust and all dualities (good or bad) and reaches liberation.

Verse 7-9: All living beings have an infinitesimal part of me as their consciousness, Krishna says.  This part interacts with the material nature through the mind and six perceptual senses.  Through sound, sight, touch, taste and sound and mind, consciousness experiences the material objects.  (usually we say the five senses–sight, sound, taste, touch and smell–here mind has been added as the sixth sense)

Verse 8: This infinitesimal part exits the old body and enters a new one like the air carries the scent.

Verse 10-11: The ignorant can’t perceive this consciousness as they are entangled in the three modes of nature, but the ones who are evolved can see it through knowledge or self realization (gyan-chakshu).  Ones who follow yog can see this with great effort but those with unprepared souls can’t see this even with great effort. It appears to be saying that the soul has to be disentangled from the three modes of material nature to be able to perceive this reality.

Verse 12-13: Know that the brilliance (tej) of sun, moon and fire are all me. I provide sustenance to all. There is a mention that I nourish plants as moon and sustain living beings as sun, but that appears more allegorical then scientific.

Verse 14: I am the digestive fire within all living beings which allows them to extract sustenance from four types of foods (ones which are chewed, licked, sucked and drunk) through combination with two types of breath (prana and apana). There is an understanding of the human or living being energy system on how the food is converted into energy. 

Verse 15: I reside in the heart (allegorical)  and cause awareness, knowledge, and even forgetfulness.  I can be known through knowledge (vedas).

Verse 16-18:  Everything can be divided into imperishable/mutable (kshar) and imperishable/immutable (akshar).  All living beings are kshar and consciousness is akshar. The ultimate cause is also described as the Ultimate Personality (uttam purusha), which permeates everything and sustains all.  I am Uttam Purush as I am beyond perishable and imperishable, I am celebrated as Uttam Purusha.  In this verse, Krishna seems to be saying that he is beyond the consciousness as well. Is he suggesting that he is beyond universal consciousness or is he differentiating between consciousness and Ultimate Consciousness?

Verse 19-20: One who understands me as Uttam Purush, understands everything.  This is the most confidential meaning of scriptures.  I had earlier raised the question on why such knowledge should be a secret or confidential (guhya).  Guhya also means deep or intricate.  So maybe it is a case of poor translation.  Maybe what is meant is that this is the deepest or truest meaning of scriptures, not the confidential meaning of scriptures.

Verse 11: