Does Nirvana really means stopping of birth and death? Does it ensures that no new one will arise again?

Does Nirvana really means stopping of birth and death? Does it ensures that no new one will arise again?

Depending on the context, there's the Nibbana-with-residue-remaining(sa-upadisesaNibbanadhatu), where the Arahant attains while still living (the Five Aggregates still exist, hence the "residue-remaining"); And there's the Nibbana-without-residue (anupadisesaNibbanadhatu), the Final Nibbana with the Arahant's final passing away. It's the latter context that guarantees no further rebirth, as per that Arahantship's signature stock phrase being mentioned repeatedly throughout the Canon:

Birth is ended, the holy life fulfilled, the task done. There is nothing further for the sake of this world." ~~ Refs ~~

You attained Nibbana while you are alive not after death. The best simile I can use is the undoing a knote. Consciousness raises due to causes and conditions. When the conditions are not there, there is no consciousness. It appears your view is similar to Brahmanism or Hinduism.

Freedom from birth and death means freedom from concepts and boundaries. Especially ones like "i am this organism". When you see beyond the organisms, then how can someone die or get born?

When you see the continuous change and the interconnectedness, how can "one arise again"?

Who is "one"? Where is it?

Buddhist theories all summed up to the point of Nibbana. They have reached the goal, gone there(Tathagat). They conclude holy life is lived and goal attained. Cessation of becoming(No new formation).

Right.

But, when asked, Do Tathagata exist after death? is absurd question.

No, it is absurd question when the absurd person asking only.

It is that our individuality arise and ceases. So, why the buddhist assume there is stopping of birth and death?

According to Abhidhamma and DN22, birth is arising, death is ceasing.

There is no personal birth because a person is the combination of many various realities arising and ceasing relatively. It is not "nothing", but there are many realities which we are thinking it is real person.

Tathagata is synonym for ocean, where waves are arise and passes away, which we calls individuality. Tathagata is the root of Tree of Samsara. It's branches and leaves are species and karmic stations respectively. So, when one attain to the root, the whole tree(Samsara) appears as mere bubbles or foam, rising and falling, absolute impermanent. So, having so, why do they preach after attaining the Root, one attain freedom form birth and death? They are not. Because from root, a new one is formed and rolled on, in this continuous existence. That's why, its been asked by some of recluse of higher wisdom, Do Tathagata (the one who goes to that, the one who ceases) exist after fall of body and life? Buddha answered: Silence! I feel that doesn't stop the new creation or new forming of individual. Hence I conclude, there is no such freedom from birth again. Why?

My assumption is that, the one who arise and ceases, doesn't exist in reality! It's like dream of someone else's and dream can't be true or real. It's only the dreamer tends to be real. Tathagata(gati of the one)literally means to merge in Brahman. The dreamer. And see this universe as mere dream. So,it appears that no new dream arise after cessation of current dream, but not so. You can control the dream but not the dreamer. The Brahman. That's why in Indian village, Saint Chokha says, 'What a miracle! The God of god is gone mad!' He is saying about Brahman. Also in Bhuridatta Jataka, The Arhats said the same thing.

If you learn Patthana in Abhidhamma, you will see how it work. And if you meditate like Pa-auk Tawya, you can see how hard is it to let it done.

When there is still desire for becoming (bhava-tanha) Nibbana isn't reached, the task not done and the source not uprooted, destroyed and so jati in another womb, taking on another stand, is to be expected.

Nobody would arise here, if no more will for becoming.

Looking aboit the foolish speculating answers, that popular under the secular justifing objected miss out "neither exist nor not exist" or both... still incapable to take no stand (jati).

"...With the ending of jati, birth, aging, death... the whole mass of suffering ends."

If there would be still birth, aging,... death, the task had failed. Pointless question and even more pointless answers at large. But it's by an element that beings find together, again and again... Full of pains, desires, restless, they feed each other like the dogs slander yoling and barking through the nights... "we are free of identification, wroof, wroof..."

Even a foolish baby-boy, not to speak of consuming pets, have no identification view... yet, age, suffer die...

Sure, the more confused the more one wouldn't see why having taken birth nor why one again and again ages, decays, not even being aware of suffering, still finding things to consume.

[Note that this isn't given for stacks, exchange, other world-binding trades, but for liberation]

Nirvana/Kensho/Satori is only a "goal" as long as you haven't experienced it. The experience conveys the one-ness, emptiness and interconnectivity of all phenomena. In some Buddhist schools, this is referred to as "the Great Death", as this reveals the "I" as an illusion.

But from that point onward, attainment has been achieved and is no longer the "driving goal" of practice. In Zen, for example, this is illustrated in a sequence of drawings called the "Oxherding Pictures". The first nine pictures illustrate the stages toward attainment. The tenth however, shows the practitioner:

10. Return to Society Barefooted and naked of breast, I mingle with the people of the world. My clothes are ragged and dust-laden, and I am ever blissful. I use no magic to extend my life; Now, before me, the dead trees become alive

A good book about life after attainment is Jack Kornfield's "After the Ecstasy, the Laundry".

As to whether attainment stops the cycle of birth and death, the answer depends on what you ask is being born and dying. If you ask for the "I", then attainment will show this "I" to be an illusion. If you ask it for the emptiness of all phenomena, the most honest answer is "we do not know". "I"