I'm pretty sure that intuition is well-understood as being due to the fact that our brains do most of their processing subconsciously. Intuition won't get you anywhere in a situation you have no experience with, but can be very valuable when you do have that experience.
So emotion can communicate knowledge, albeit not 100% reliable?
I don't know what you mean by "nonduality".
AFAIK It is a supposed state of consciousness attained by practicing
Advaita Vedanta (a form of Hinduism made popular by Shankara).
There is no scientific account possible of any sort of union with any supernatural.
But there is the psychology of religion, for instance neurotheology.
I have no idea what you mean by "atman=brahman"
It is a way of saying, in hindu terms, that the individual soul is one with God. A similar Hindu way would be to say that Purusha (absolute consciousness) and
Prakriti (man, material existence) are one. According to book mentioned below at least.
but as those appear to be religious terms, I sincerely doubt that they have any relationship to science, or reality.
Well science can study neural correlates of religious states (trance, vision, certain hypnogocic sleep states, meditation etc) and give an interpretation of them in terms of brain dynamics.
I mentioned unitive awareness (in its various manifestations) after reading this book:
History of Mysticism by Swami Abhayananda who claims that various sages have has the same experience through the ages. I was wondering if people who claim such unitive awareness experienced by practitioners of various faiths have been studied by PET of FMRI.
Also IIRC "unitive awareness" was mentioned in the book on
cognitive archeology Inside the Neolithic Mind, by Lewis-Williams and Pearce, as another "altered state" form of experience (alongside
geometric hallucinations, mentally travelling through tunnels, and spirit visions) which the human mind is psychologically predisposed to under certain conditions. This understanding can allegedly be used as an explanatory tool in interpreting ancient religious remains. This book by atheists, not swami.