When the Upanisads speak about the self in this may they refer to the Supreme Self, not the individual self.
Yes, it refers to the universal self. Hence why it also says
'Ayam Atma Brahma" - My Atma is Brahman
The Atman of all beings is the same. All living entities are Jivatmans, i.e., fragments of the one single Atman. The actual self of all Jivas is the Atman. In the same way the self of all rays of the sun is the sun itself. The Jivas are in essence all identical.
Everyone has powers to manipulate something. Yogis can acquire much more power than ordinary beings, but never complete power. Complete power is the hands of the Supreme God only - fortunately. We would just create havoc, that’s why our powers have to be limited.
If you could perform even half of the siddhis Patanjali describes you could not be called limited. Here are just some of the powers Patanjali describes:
Knowledge of the entire solar systems, star systems
Knowledge of all of ones past births and past
Knowledge of the future
Knowledge of the thoughts of all other beings
Knowledge of the entire constitution of ones body
The power of invisibility
The power of living without food or water
The power of invincible strength
The power of clairvoyance, clairaudience, clairsentience
The power of entering and controlling any other body
The power of levitation and flying
The power of teleporting to any point in space
The power to control the gross and subtle elements
The power to increase ones size and decrease ones size
Here is where Patanjali makes it explicitly clear that the power one gains are unlimited:
3.48: Mastery over the sense organs is gained by samyama on the senses as they correlate to the process of perception, the essential nature of the senses, the ego-sense and to their purpose
3.49: From that, the body gains the power to move as fast as the mind, the ability to function without the aid of the sense organs and complete mastery over nature(prakriti)
3.50: By recognition of the distinction between sattva(the pure reflective aspect of the mind) and the Self, omnipotence and omniscience is gained.
3.56: When the tranquil mind attains equal purity to that of the Self, there is absoluteness.
Simply put, Patanjali is saying you can eventually become a omniscient and omnipotent being. If that is not a god, then tell me what is?
Where do the yogis get their power from? They have to undergo severe austerities to get them.
According to Patanjali these powers all come by themselves as a result of ones spiritual development, they need not be strived for.
3.34: Or, the knowledge that dawns by spontaneous intuition(through a life of purity), all the power comes by themselves
4.1: Siddhis are born of practices performed in previous births, or by herbs, or through mantras, austerities or samadhi
There are indeed countless examples of how ordinary pious humans have developed powers and abilities, like monks, saints etc
And Patanjali warns that the eight mystic siddhis are actually obstacles on the path of self-realization. It’s another snare of maya. If you go for them your whole progress in the matter of self-realization is ruined.
No, Patanjali warns that if we linger on the various siddhis they will become obstacle to the final goal which is total realization of ones absolute self.
Everyone has his or her own project for becoming God and exploit nature and other beings. This is the whole struggle of existence because we are all like this. We have to give up our idea of power and control before we can become self-realized.
If you give up your idea of power and control, then you will never become a god. Isn’t the Yoga about the total mastery over body, mind and nature? Give up and forget about becoming a god. You seem more content in worshiping god than becoming a god.
The particles or fragments never become one with the Supreme Self, they are always one with it. The self is eternally unchanging, it does not become anything else than what it is now. The fragments exist eternally as fragments and the whole exists eternally as the whole.
Do you realize the problem in setting up a dichotomy between the whole and the parts? The whole pervades all the parts. The whole is never separate from the parts. In the same way each droplet of an ocean is pervaded by the ocean, it is never separate from the ocean. In the same way every jiva is pervaded by the Atman, they are never separate from the Atman. The essence of every Jiva is the same Atman.
Continuing with the ocean example. The ocean gives rise to droplets, foam, waves, pools, rivers, but foam, waves, pools, rivers are just name and forms of the same substance of the ocean. In actual fact they are all the same ocean, there is no such thing as foam, rivers pools, rivers really. Likewise, there really is no such thing as jivas, space, time, energy, mind, matter and bodies of any description, it is all that one Brahman expressing itself in infinite forms. Hence the Upanishads declare: Aham Brahmasmi - I am that Brahman.
“The living entities (jiva) in this conditioned world are My (mama) eternal (sanatanah) fragmental parts (amsah). Due to conditioned life, they are struggling very hard with the six senses, which include the mind.”
(Bhagavad-gita 15.7)
This can also be interpreted to mean that Krishna is speaking from the perspective of a self-realized god. All self-realized gods would speak the same - “All is a part of me” “I am the ALL” Remember Krishna actually even says, “I remember all my past lives” which means Krishna too went though the cycles of birth and death as every soul has to, before he attained full realization in one of his births and could speak like a god.
What I am saying is: Don’t worship Krishna, follow Krishna example and become a god yourself. You do not need to worship anybody mortal. Become a god and let others worship you 
The tendency for worship is indeed also a primal instinct and again we can see from the beginning of history of humans that humans have been worshiping something or the other, natural phenomenon like fire, animals, trees or other humans, or conceptual things like concepts of god, images, ideas. In order to understand why humans do this we need to look into the psychology of humans and their motivations for worship, rather than the objects that they worship. Then we will realize there is something inherent within human psychology which recognizes subconsciously something greater, a higher power, but not as something which is externally existent, but something which is our essential nature. This is something the Vedic Risi’s also realized: There IS a higher power and this higher power is intrinsic to our essential nature - Atman = Brahman.