I always hear about the principle of life and death. That death is necessary to one's life. Not only to give your life meaning and balance but to also to give balance to mother nature. This is further supported by those phrases like nothing lasts forever etc. To be honest I never heard about the concept of immortality to be preached about like the concept of life and death from very old gurus/saints/philosophers (200 -300 years ago as an example). Are there any who support the idea of immortality?
I'm not sure I understand your question. If you mean immortality in the sense of life "after" death, then yes, most philosophers in the Western tradition would hold some version of that belief, from Plato's Phaedo to Descartes, to Kant and probably Hegel, and any other philosophers of the Christian faith, up until the rise of secularism in the 19th century.
There are undoubtedly philosophical "proofs" of life after death, though I haven't read any. I'd imagine Augustine and Aquinas may have produced some, though even in these cases, I don't think the question entered much into philosophy per se. Hume famously refuted such "miraculous" events as the resurrection, but Locke, his predecessor among British empiricists, accepted it on the basis of four personal testimonies, which even he believed to be adequate evidence.
Of course, skepticism is rife in philosophy and you can't prove a negative, so I think most philosophers leave such issues to faith. Today, I imagine the majority of professional philosophers do not believe in "life after death." Or take a wait and see attitude.
If you mean immortality in the sense of just not dying, retaining a continuous body and identity, the apparent absence of undead or immortal beings does not provide much room for debate. Philosophical speculation on the implications would be interesting (probably there is some) but imagining the consequences has been largely left to literature.
We do now have a lot of speculation about the Singularity and the possibility of a form of "uploaded" immortality. The chief proponent of this idea is the inappropriately named Ray Kurzweil. If there is a philosophical champion of the value of death for a proper life, in the manner you describe, that might be Heidegger.