This isn't related to enneagram as far as I know, but my thoughts to your questions:

1. I'd say essence represents the core self where atman is that core self in relation to to oneness. I've had non-dual experience but at the same time that feeling is experienced from your perspective of I. Maybe the feeling of I dissolves but at the same time, it exists. It is what we return to.
2.i don't think the essence is the same as the soul. Jung kind of correlates the soul to all the experiences we've collected or been through. I think the essence can shed these experiences if desired possibly. At least I would think it could be so. May not mean they don't exist but our attachment to them would cease. It's also possible that our soul makes our essence what it is, so there's that.
3. I think the spirit or essence is connected to our higher centers through the heart and mind?

 

Thanks dor reply. I agree with you thet I si not dissolves, but sometimes i feel like that. It is not clear to me how the enneagram defines the essence? Does it represent core self/individual self or does it represent some universal aspect? Does everyone have a unique essence or is the essence the same for everyone? I also wonder, are virtues the same as essential qualities?
Gurdjieff he said that the essence is the substance from which the soul grows. For me, it is a very powerful statement, because then it gives the enneagram a much deeper purpose. But I have seen different definitions of essence in different books. I even read somewhere that they connect the essence with the Tao, which are completely opposite concepts.

 

The concept of essence in the Enneagram appears through two different sources: Gurdjieff and Ichazo.

Gurdjieff is sometimes brought into the Enneagram by those who relate the Enneagram symbol back to Gurdjieff. Though, Gurdjieff actually had nothing to do with the types. Here's an example link: The Enneagram of Essence and Personality - New York Enneagram

Ichazo, who initially placed the types on the symbol, brings in the concepts of essence through his holy ideas and virtues. Although Ichazo's concepts form the roots of the types, over the years the popularization of the types lost much of what they were originally about. Here's a link about Ichazo's concepts: Traditional Enneagram (History) — The Enneagram Institute

As I understand it, Ichazo saw ego or personality as forming when the self begins to experience itself separate from the world.

"We have to distinguish between a man as he is in essence, and as he is in ego or personality. In essence, every person is perfect, fearless, and in a loving unity with the entire cosmos; there is no conflict within the person between head, heart, and stomach or between the person and others. Then something happens: the ego begins to develop, karma accumulates, there is a transition from objectivity to subjectivity; man falls from essence into personality." (Interviews with Ichazo, page 9)

 

I think there is not good definition of essence. If I understood correctly, the holy idea is a mental non-dual insight of one element of essence (there are a total of 9 possible insights into the nature of essence). And virtues represent the inner feelings that are the result of that realization (every holy idea has its one virtue). Depending on which enneagram type I belong to, one holy idea and one virtue will be the main one for me. They will represent the main quality of my essence (although it is possible to realize all nine).
Now comes what bothers me. If holy ideas represent our non-dual perceptions of essence, then essence belongs to non-dual experience. So the essence is the universal self. In Gurdjieff's teaching, essence represents the core part of who we are, on an individual level. The first step in inner work is to get rid of the ego (bad crystallization) and to crystallize our selves on the basis of essence (to create our true self, soul or one I).

 

Personally, I don't bother with concepts such as essence. IMO, getting lost in concepts and definitions is part of the problem in the first place.

Strangely enough, this video with Russ Hudson titled "Exploring Personality & Essence" just popped up in my YouTube recommendations. Russ has a background in the Gurdjieff teachings and of course is a well-known teacher/author of the Enneagram types. I have no interest so I didn't watch it, but maybe it's relevant to this post.