2) Explain in detail what the illusion of separate self is, when it starts and how it works.
The illusion of a separate self is a mental construct. It is a conglomeration of thoughts and memories and mental habits that reference a fictional character called I or me. This idea that there is a separate entity that experiences something is embedded in language. "I think" "I am hungry" "I am sad" can be a convenient way to communicate what is happening in the moment. Until the underlying assumption that there is a real somebody there who is hungry or sad is questioned, this pattern of language serves to reinforce the illusion of a separate self.
I don't know exactly when the illusion starts. I don't know if there is something fundamental to human neurology that is reflected in our language or if our language influences our neurology. Probably both. What I have seen is that as children learn how to speak, we train them to believe in the separate self.
As a child I learned my name and the basic rules of ownership. While some rules seemed arbitrary, the one object that everybody agreed belonged to me was the body. If I said "my cigarettes" I was quickly corrected. Toys were debatable. Sometimes they were mine, sometimes not. If I held up my hand and said "my hand" nobody ever objected.
The lesson was learned. This body that I can move is mine. Everything that is experienced within the body must also be mine. Thoughts became my thoughts, emotions my emotions, pain my pain, and so on. The idea of a separate self that is defined by the limits of the physical body was established. From there on life was experienced as "me in here" and "everything else out there." That is why the illusion of a doer is so strong. As long as I believe in "I", if it happens in my body, I must be doing it.
The illusion stays intact because it is accepted as reality until it is questioned.
3) How does it feel to see this? describe in detail
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It is a great relief to recognize the mistake. As long as I was searching, I felt trapped inside the body and kept trying to find out how to connect "my consciousness" with "Consciousness". Recognizing that "I" is just a sticky thought in the mind that likes to glue itself to other thoughts and is mistaken for an actual being opened the door for the seeing that there is no such thing as my consciousness. Consciousness is. Watching happens. Thinking happens. Nothing to be done, nothing to be connected.
4) How would you describe it to somebody who has never heard about this illusion but is curious about it.
It would really be context dependent. If I think about all the times I heard a metaphor like "here you are living in poverty and you don't realize you are a millionaire" or "The chief of police can't find the murderer because the chief of police IS the murderer he is searching for" I just laugh. Now that I have seen through the illusion, I totally get what they were pointing to. Really, though, it is like trying to describe the taste of a lemon to someone who has never tasted one. No matter how good the description is, the person has to taste a lemon to know how a lemon tastes.
If the opportunity presents itself I would ask a question that causes a gap because it is the glimpses in the gaps between thought that allow the illusion to be seen for what it is.