Is there a particular theory against the philosophical possibility of eternal
I agree with Richard Heck's response, but would like to respond to the first part of this question. I think there are some fairly persuasive reasons for thinking there is no such thing as eternal life--though I doubt that an argument could be given to show its impossibility. So:
(1) If we agree that the body dies and is ultimately destroyed as an entity, then the only way there could be eternal life would be if the living self is entirely distinct from the body. But the kind of mind-body dualism that might make this possible has been shown (in many ways and by many philosophers) to be at least profoundly problematical, if not simply incoherent. Indeed, many philosophers regard the very idea of "disembodied existence" as problematical, if not simply incoherent.
(2) Even if survival of death means re-embodiment in some form, it would still appear that the living self is entirely separable from the body that dies, so that does not solve the problems of (1). Similarly, there seem to be fairly strong conceptual reasons for supposing that theories of reincarnation or transmigration of consciousness are incoherent. There are many technical reasons for this, but for an intuitive grasp of their gist, consider: Is it really imaginable that you could be both YOU and also A CHICKEN (for example)? How can a being have BOTH a human and a chicken form of consciousness (whatever that might be like)? If "what it is like" to be a chicken is something in principle not available to you, then actually being or becoming a chicken is something that in principle cannot happen to you--either you would not really be a chicken, or else you would be destroyed in the process.
Unless there is some other (coherent) way to conceive of eternal life, then I think you would do well to worry about the one (mortal) one you have. Last chance!
Is it possible for one to possibly know what exists after death? As humans, with
Some people think they do know what exists after death. As Alex notes, "Nothing" is one option, and some people believe they have strong enough evidence for this view to make it a reasonable belief, and perhaps even to count as knowledge. On the other side, there are people who would claim to know, on the basis of divine revelation, that they will survive the deaths of their bodies. Presumably, not both camps can be right, and both camps might be wrong about their claims to know. But I don't see any general reason, absent consideration of the details, for supposing neither of them could know.
Perhaps one wants to say that neither camp can really know, on the ground that truly conclusive evidence isn't available. But truly conclusive evidence is rarely available for anything, and yet we claim to know lots of things. That is to say: The claim that it is not possible to know what exists after death seems to be based upon a general sort of skeptical challenge that, allowed to run free, would undermine all claims to knowledge.
I don't know if this is a good question, but is it morally correct to execute
If people did not fear death, is it likely that religion as we know it would not
That question can be taken in many different ways. One way is historical. I'm in no position to answer that question. Another would be sociological. I'm not in a position to answer that question, either. Part of the problem here is that I'm not an historian or sociologist. Another is that there's substantial vagueness in the phrase "religion as we know it".
Here's a different question I can answer: Does relgious faith have to be bound up with or somehow a consequence of one's fear of death? The answer to that question seems to me obviously to be "No". I suppose there are particular forms of religious faith that are so bound up with a fear of death, and perhaps these are the most visible in American public life or the most salient to non-believers, but there are plenty of forms of religious faith that are not.