Buddha's knowledge of prior births

The Pali suttas appear to explain the word 'birth' ('jati') as the mental generation of the mental idea, view or 'assumption' of 'beings' ('satta') or 'self-identity' ('sakkaya'); that, apart from 'view' or 'conceptual thought', there are no 'beings' to be found. It seems each time the mind believes it is a 'self', that is another 'birth'.

Therefore, when the Buddha recollected his previous 'births', this could have been the recollection of each time in his life when he truly believed something to be 'him' or 'belonging to him' (such as when he was 4 years old & had a fight with another child over a toy, which he believes was his toy).

If the word 'birth' is taken to mean 'ego birth' then it is easy to understand how the Buddha, on the night of his enlightenment, recollected the millions of times the mind in the 35 years prior to the Enlightenement believed it was a 'self'.

or was it just mind hallucinating because of hunger, thirst?

No. You are mixing up chronology of events. The Buddha gave up extreme asceticism before gaining Enlightenment.

Did Budhdha really got to know his previous births

Yes. By entering the 1st jhana, one can even recall one's past lives. The below passage from MN 36 indicates Buddha went to 4th jhana before doing so, recalling many more. I would refer to the book Mind Experiment by Bavo Lievens for references on Buddhist texts, as well as beautiful Buddhist cosmology and how to go about doing this. Go to page 80.

Here is an excerpt from MN 36: <-- read the full sutta

"When the mind was thus concentrated, purified, bright, unblemished, rid of defilement, pliant, malleable, steady, & attained to imperturbability, I directed it to the knowledge of recollecting my past lives. I recollected my manifold past lives, i.e., one birth, two...five, ten...fifty, a hundred, a thousand, a hundred thousand, many eons of cosmic contraction, many eons of cosmic expansion, many eons of cosmic contraction & expansion: 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure & pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure & pain, such the end of my life. Passing away from that state, I re-arose here.' Thus I remembered my manifold past lives in their modes & details."

If ever you get a chance, @I don’t know, please try to read the following sutta. It is rather lengthy, so let me give you the bit that is relevant to your question. DN 2 - Samaññaphala Sutta: The Fruits of the Contemplative Life http://www.accesstoinsight.org/tipitaka/dn/dn.02.0.than.html

The three knowledges, as described in DN 2, are:

Recollection of past lives (pubbenivāsānusati-ñāṇa): "He recollects his manifold past lives, i.e., one birth, two births, three births, four, five, ten, twenty, thirty, forty, fifty, one hundred, one thousand, one hundred thousand, many aeons of cosmic contraction, many aeons of cosmic expansion, many aeons of cosmic contraction and expansion, (recollecting,) 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose here.' Thus he recollects his manifold past lives in their modes and details."

Knowledge of the passing away and reappearing of beings (cutūpapāta-ñāṇa): "He sees — by means of the divine eye, purified and surpassing the human — beings passing away and re-appearing, and he discerns how they are inferior and superior, beautiful and ugly, fortunate and unfortunate in accordance with their kamma.

Knowledge of the ending of mental effluents (āsavakkhaya-ñāṇa): "He discerns, as it has actually come to be, that 'This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress... These are (mental) effluents... This is the origination of effluents... This is the cessation of effluents... This is the way leading to the cessation of effluents.' His heart, thus knowing, thus seeing, is released from the effluent of sensuality, the effluent of becoming, the effluent of ignorance. …”

The first two of these knowledges, even though they comprised part of the Buddha's Awakening, are mundane, in that people may develop them without necessarily attaining any of the transcendent paths and fruitions. Thus they belong under the category of mahaggata dhamma, as they are based on the attainment of jhāna either in this or in a previous life. The third knowledge, however — because it describes the arising of the transcendent paths and fruitions — comes under the category of lokuttara dhamma, and is the only one of the eight knowledges to do so.

DN 2 describes the remaining five knowledges as:

Insight knowledge (vipassanā-ñāṇa): "He discerns: 'This body of mine is endowed with form, composed of the four primary elements, born from mother and father, nourished with rice and porridge, subject to inconstancy, rubbing, pressing, dissolution, and dispersion. And this consciousness of mine is supported here and bound up here.'"

Mind-made body (manomayiddhi): "From this body he creates another body, endowed with form, made of the mind, complete in all its parts, not inferior in its faculties, just as if a man were to draw a reed from its sheath."

Supranormal powers (iddhividhī): "He wields manifold supranormal powers. Having been one he becomes many; having been many he becomes one. He appears. He vanishes. He goes unimpeded through walls, ramparts, and mountains as if through space. He dives in and out of the earth as if it were water. He walks on water without sinking as if it were dry land. Sitting cross-legged he flies through the air like a winged bird. With his hand he touches and strokes even the sun and moon, so mighty and powerful. He exercises influence with his body even as far as the Brahmā worlds."

Clairaudience (dibba-sota): "He hears — by means of the divine ear-property, purified and surpassing the human — both kinds of sounds: divine and human, whether near or far."

Mind-reading (cetopariya-ñāṇa): "He knows the awareness of other beings, other individuals, having encompassed it with his own awareness. He discerns a mind with passion as a mind with passion, and a mind without passion as a mind without passion (etc.)."