As per Advaita school of Vedanta; living entity is identical to supreme brahman. Advaitins generally interpret 'Aham Brahmasmi' as 'I'm supreme Brahman'(please correct me if i'm wrong). We are Brahman but right now covered by ignorance(Maya).
1.Does that mean Maya is superior to brahman?
2.Vedanta Sutra(1.1.2) says 'Janmadyasya yatah' ; meaning 'from which origin etc'.That would mean Maya has also come from Brahman. Then how can(/has) this maya taken over Brahman?
This is the absolute reality. In this level neither Ishwara nor Maya exists. Only Brahman exists in Sat-Chit-Aananda Swarupa. Here Sat means pure existence of Brahman, Chit means pure consciousness of Brahman and Aananda means infinite blissfull state of Brahman. There is neither any creation nor any destruction in this state. Just Brahman exists in Satchitaananda form.
This type of reality is called Ishwara Shristi. This is the reality at that level when universe is covered by Maya of Ishwara. Maya is the potential energy of Ishwara. For eg. We see Mirage in desert. That is illusion. We know it but we can't remove it by knowing it. We can just understand that it is illusion. Similar is the level of Vyavaharika Satyam. We can only understand Maya of Ishwara.
Ishwara himselfs creates this Universe by the power of Maya. Ishwara does so because creating is his nature. Ishwara is neither inside the creation nor outside the creation but Ishwara is itself creation. Ishwara creates with the help of Maya. Maya has two powers.
This is the covering power of Maya. By this power the beings in creation forget that they are 'Brahman'.
This is the projecting power. By this power the universe which we see is projected in this way we see and observe.
Is Ishwara under influence of Maya ?
No, Ishwara is not under influence of Maya. Although Ishwara is Saguna and saguna form is taken by the help of Maya. But still the nature of Ishwara is defined as Sarvagya (ie. All knowing). Hence Ishwara isn't deluded. But he uses Maya power to be in Saguna form and for creation.
2.6.1 He (the Self) wished, "Let me be many, let me be born. He undertook a deliberation. Having deliberated, he created all this that exists. That (Brahman), having created (that), entered into that very thing. And having entered there, It became the formed and the formless, the defined and the undefined.."
So he wished and he became many. So he himself is the creation. So everything in this Vyavaharik level (including ourselves) which we see is simply Ishwara himself.
What is the origin of Maya?
Maya is due to Vaasanas (desires) which are accumulated in the mind. How desires originated ? Desires are originated because it is originating now. It is seen through 'Pratakshya Pramanam' ie. Direct Perception. We can't trace first origin of it. But it originated because it caused Maya and Maya caused Ishwara Shristi. And as we can see Ishwara Shristi right now here, thus it originated. As we can't trace first origin of vasaana and hence we can't also trace origin of Maya. And Hence Maya is called to be existing from beginning. But it isn't in Paramarthika level.
How we got individuality ?
In Paramarthika level there is no individuality as only Brahman in Satchidananda Swarup exists there. But in Vyavaharik level we see individuality. As Vyavaharik level is due to Maya of Ishwara. Hence it is responsible for our individuality. As Upanishads declare 'he became many...'. Thus at this time individuality arose due to Aavaran(covering) power of Maya. It is described as Akash GhatAkash Vaad. Here Aakash is infinite and Ghat akash means part inside infinite. Due to influence of Maya a small portion called Ghat-Akash is covered by Mind Intellect and other sheath to satisfy it's desire (called vaasanas). Individuality arises at this stage.
The standard example given to represent creation in Advaita is dream world. We see dream due to unsatisfied desires remained as impressions in our mind which are called Vasanas. Due to Nidra Shakti (analogous to Maya Shakti) we see dream and due to Vikshepa(projecting power) we create a new dream world. Just as Ishwara creates this world by himself (multiplying). Due to Anavaran (covering) power of Nidra shakti (ie. Maya) we forget we are dreaming and as we ourselves are also in dream world and now we began to think world and us as separate. This process continues until we possesses sharp intellect with Jnanam. Thus creation by Ishwara is analogous to our creation of dream world.
He may go on doing normal activity inside body to destroy Prarabdha karamas. But he is not affected by such Karmas as he knows he is not that body, mind and intellect but he is the Supreme Sat-Chidananda-Brahman.
There is no meaning of death here. It is just casting of Sthula Sarira. As he don't possess desire he isn't attracted to have any new Sharira/body. So he don't have rebirth. He is in the highest blissfull state so he doesn't desire to do any other thing or to get reborn in Samsara or other.
1.4.10 And to this day whoever in like manner knows It as, 'I am Brahman', becomes all this (universe). Even the gods cannot prevail against him, for he becomes their self.
But he rarely chooses to do anything as he is in the most blissful state. So anything he does is of lower bliss than that state. But he may also, as Suka in Mahabharat did so one time. He pronounces 'Bho' and entire universe pronounced 'Bho' as he had became self of all. He did it to calm grieving Veda Vyas.
Thus for other people after moksha also he gets individuality as moksha/liberation can happen while being in Sarira also. But for him there is no individuality as he donot identify himself as body, mind and intellect. After death also sheath of mind and intellect are there. But he may choose only to live in Paramarthika level by casting off mind and intellect thus we may here call it lost it's individuality. But there is no meaning of calling it losing individuality as individuality itself was illusion at the first time and creation itself took place by " he became many...".
Advaita Vedanta says that ignorance of Brahman has created this world. Ignorance, which is the opposite of knowledge (jnana-virodhi), is not something negative. It has a positive character (bhavarupa). It has two powers: (1) the veiling power (avarana-shakti) and (2) the power of projection (vikshepa-shakti). Ignorance has the power to cover or veil the Reality, which is Brahman, and also the power to project this world on the veiled or covered Reality. The world is the product of mula-avidya. The individual ego, which is part of this world, is also the product of mula-avidya. Consciousness associated with this ego is called the Atman or the Jivatman. Between the Jivatman and Brahman (Paramatman) there is a thin veil of ignorance. It is like a cloud that does not all an individual to see the sun. In this analogy the Brahman is the sun and the patch of cloud is the ignorance of the individual. When this individual's ignorance is dispelled by the knowledge of Brahman, he or she will have the experience of Brahman.
Gaudapada's name is specially associated with the theory known as Ajata-vada. This theory may also be called the theory of non-origination. According to Ajata-vada, the perceptual world in which we exist was never created. This theory rejects all causality. It does not accept that there is any cause or source of this perceptual world.
Shankaracharya recognizes three kinds of existence (satta): (1) empirical existence (vyavaharika satta), (2) apparent existence (pratibhasika satta) and (3) ultimate existence (paramarthika satta). He recognizes the empirical existence of this world but not its ultimate existence. Only Brahman has 'ultimate existence'. Compared to Brahman this world has 'empirical existence' only. Therefore this world is only an apparent transformation (vivarta) of Brahman. It is not a real transformation (parinama). The word mithya means something that has been imagined in Brahman.
From the point of view of Advaita Vedanta, maya and avidya are the same. Just as avidya or ignorance has the powers, as it were, to hide Brahman and project something else, such as the world, on it, so also maya, as it were, can cover up Brahman and project the world onto it.
Maya cannot really cover the Reality that is Brahman. A patch of cloud can never cover the sun. It only covers the eyes of those who are looking at the sun. In the same way maya covers our knowing ability and thus obstructs our knowledge of Brahman.
In any act of knowing, the 'knower' and the object known' have to be separate from each other. They cannot be the same. In order for us to know maya, it has to be separate from us. Individuals like us are the products of maya and we are all posited within the domain of maya. Maya and we individuals are not separate from each other, just as chocolate and a bear-shaped chocolate candy are not different from each other.
As we are identical with maya, we cannot know maya. For this reason, maya is not only unknowable; it is inexplicable as well (anirvachaniya).
According to Advaita Vedanta a jivanmukta, or one who is liberated here and now, has realized that Brahman alone is real and the world is illusory. Therefore, one may argue that experience of Brahman there should not be any awareness of the physical body or the world around it. But the continuance of the physical body or the world is not incompatible with the idea of liberation according to Advaita Vedanta. Before liberation, one surely thinks of oneself as the body. After liberation, however, one realizes that the physical body and the world have only an illusory appearance. Even though they appear to exist they do not really exist. From the viewpoint of Advaita Vedanta liberation is only a change of perspective. Since the physical body is not real, its continued appearance, or its eventual disappearance, is no problem for the jivanmukta. To a jivanmukta the body and the world are like a dream. The only difference between an ordinary dreamer and a jivanmukta is that the ordinary dreamer, while dreaming, does not know that it is a dream. But a Jivanmukta always knows that he or she is the dreamer.
Is Maya superior to Brahman?
This question can not be answered as Maya is unknowable and inexplicable. At the level of Ishvara, Maya may be thought of as His power.
Has Maya taken over Brahman?
Again this question has no answer since Maya is unknowable and inexplicable.
Does a living entity retain individuality or merge in Brahman? If the answer is yes, then when did he get it the first time?
The Jivanmukta finds that the universe, individuality etc are all unreal. It is not whether a Jivanmukta retains individuality or merges with Brahman. The concept of merging is a dualistic idea. The Jivanmukta is himself Brahman. So the concepts like individuality and merging do not exist in the state of moksha.
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