The Core-self.
The first paragraph is a loaded question, like a loaded gun. If someone hands you a loaded gun with the mouth of the weapon pointing towards you, then if you hold the gun it is likely that it will fire off and then you will be dead, but you will have killed your body by your own action.
So in these questions you are handing a gun with the nozzle pointing towards me. This kind of gun transfer is of no interest to me.
Before answering these questions, you would have to declare your own ideas on the core-self, the variegated transcendental atmosphere as you termed it and also the mundane energy, because for a question like this to be posted you must already have ideas on these topics.
If the ideas are not based on your direct experience, then we are in a quagmire because everything we say would be theoretical because you will not be able to give us eye-witness statements.
The honest thing to do I feel is to first state your ideas and then to ask if my ideas are similar to yours, rather than to assume that I have the same ideas.
To be fair you would first have to write definitions of your technical terms and then ask the questions because then I am, also other readers would be, on the same page with you. Otherwise when you say apple and I am thinking goat, we will never have any clarity in a conversation.
Let us deal with your 2nd question:
Are there core-selves, who are causelessly without developed transcendental senses, while there are those who causelessly have such senses?
This question is also a bad question because it seems to be that it is based on your already having definitions of certain terms and you have not clarified your definitions. It would be crazy for me to assume that I know your definition and even if I did, then what about other readers?
However from the view point of inSelf Yoga™ we begin by perceiving the core-self as one of the components of consciousness which is in the head of the subtle body. With that core-self which is the observing principle in that subtle body, there are adjuncts or sophisticated sensing psychic sensing devices. In that condition, that core self has no limbs and sense but it is only a point of illumination, a microscopic something which is higher in vibration than of the psychic adjuncts. It can experience itself there as a microscopic something from which a sort of energy or light pours out constantly and perpetually.
This observing principle we identify as being what is called atma in traditional usage in yogic text from India.
So that is where we are beginning in inSelf Yoga.
Limbs and sense are extraneous or extras add-ons based on this observing self being linked to these psychic and physical phenomena. When these extraneous aspects are developed into something physical, we say that this self is a physical body and when it is developed into something subtle or psychic, we say that it is a subtle body.
The whole idea behind inSelf Yoga is to cause the student to realize this as the most basic understand of the self which can be experienced directly through meditation.