Here's another way to look at Religion: from the biological basis (and then working up). It may help if you can see obvious differences with your aliens and humans hence may mould your aliens religion differently.
It's an argument that being religous is a natural 'state' for a human.
I must point out that I am a militant agnostic atheist - or is it an atheist agnositic militant...anyway I am really no expert on religion and really do not have a spiritual bone in my body. But I do find it fascinating to think about...
(WARNING DOES CONTAIN A BIT OF SPECULATION!)
The Basics
Self-Aware Consciousness. As I believe Interface pointed out, the core mystery of 'I know that I am' is really the starting position of all religion. It naturally splits the universe into two parts: me and the rest of the universe. Even my body appears to be 'driven' by my self-aware thoughts (why not call it a 'soul'). Does this duality not feel 'natural'?; flesh and blood animated by a seperate 'soul'. And I'm sure our ancestors on the savannah when seeing a dead member of the tribe would have intuitively made assumption the process of death involved the splitting of this duality - after all the flesh remains but the person is gone...
Imagination and irrational beliefs. The problem with our amazing self-aware consciousness is that we can only really know what we think, everything else out 'there' is unknowable. However this is where belief comes in to rescue us. We hypothesis, imagine, plan, estimate, assume and ultimately test them via experience. To do this is to build a 'working' reality.
This would appear to be the blue print for the scientist, but we are awash with irrational beliefs. Why?
Well there are possibly good evolutionary reasons for us to be irrational - if you are stalking an antelope in the long grasses, a strange rustle nearby might be big cat hunting you - hence you carefully make sure it's not a lioness or scuttle to safety in terror. Now nine times out of ten it could be explained by, say the wind. But the person that believes that it's just the wind all the time will get caught out when it is a lioness/leopard on the prowl (and will pay for it!)
So far so good, this is the mundane experience...
The Other Realm and altered states of the mind. What I've sketched out above is the everyday. To fully understand religion I believe you have to be aware that he human mind operates on other levels. We all dream every night (whether or not we remember), we can experience waking visions, we meditation to lose our sense of being, we imbibe drugs to alter our state of mind. What is important here is that these can be profound and transforming experiences to the individuals and more importantly - they are actually
not necessary at all for everyday mundane life.
How to interpret these strange experiences?
Well, science today that these are caused by biochemical imbalances (such as consuming alcohol or shrooms) , diseases or faults in the brain (ecstatic visions caused by epilspesy say, or feverish hallucinations). Essentially a disruption to normal function. Fair enough, seems reasonable!
But an equally valid explanation (especially for those people 50,000 years ago) would be that this is also another 'different' realm - a 'spirit' realm that does not directly interact with our waking reality, yet somehow indirectly touches upon it. Through experimentation there are paths reach these places. Note I called this the spirit realm, because it just mostly impinges on our thoughts - the soul...
This second view is still valid today to some degree, if you so wish - e.g. the process of hynagogic hallucination may be a sleep malfunction or it may be a mode of the brain that is really in communion with some other realm beyond the physical (like an radio antennae tuned to radio waves)
Also note that our ancestors having decided that they were in contact with this Other Realm might also conclude that everything is also in contact: e.g. animals, plants, bodies of water, thunderstorms etc. (the beginings of animism...)
Social bonds. The development of large brains and minds has one major drawback - it takes a long time to nuture and a long time to develop the necessary experiences to survive as an adult. Hence evolution moulded us as social animals to overcome this deficit. The older teach and show the younger. This hierachry when imprinted on our self-aware consciousness naturally makes us extend this out: If parents look after us, and grandparents look after the parents and the group, who looks after them? Does some 'Super' parent out there ensure that there is always nice fruit or that the herds of deer are plentiful. (Of course what happens when food runs out and you starve - have you angered them?)
To try and think about this differently: How would a tiger, with much weaker social interations think about this? Instead of some loving 'super-parent' out there looking out for him, would he instead imagine some savage 'super-predator' out there actively trying to hurt him at the core of his personal 'reglion'?
Putting it all together: Shamen
I must make this clear - this becomes even more speculative - we really just don't know and may never know why our ancestors did what they did. Ever. But here's my take!
Perhaps 50,000 years ago or even more we were: self-aware with a dualistic soul/body, aware of another realm via altered states of the mind, possibly believing in 'super' humans in the spirit world who may be benevolant/angry. (and of course able to communicate all these ideas via language with each other, but we'll assume that!)
It would be natural to assume therefore that as the Spirit realm is non-corpereal, that death could be a process that allows our soul to travel over to the Other Realm leaving the body behind. I think you can see this in the process of burying the dead and graves - it was necessary for the death to be done 'properly' to aid the soul in the transfer across (There of course are other beneficial reasons too: To remember a life and to grieve etc...)
As the Other Realm appears to impact us and our reality it and it was a profound and important place it became necessary for there to be a way for us to travel across
and come back again. So the first practitioners, lets call them Shamen, would travel the astral and spirit dimensions to commune with the ancestors or 'gods' to ask questions, divine answers or plead with these powerful beings.
(Note at this stage the Other Realm will reflect the culture of the people that travel there, as how people live
now is obviously the 'best' way for humanity to live and their ancestors and gods must do the same, albeit more perfectly.)
These shamen were special people. They were gifted or skilled in the rituals that required them to cross the barrier that most people in society would only cross by accident or at death. So it was very difficult - they ate poisons or sun-danced for days fasting and exhausting themselves.
For example cave paintings in Europe, possibly used by shamens to commune with the spirit world after consuming hallucegenic drugs were not in easily accessible areas - many were in deep in the earth, as if the journey there was part of the process. Not only did they paint animals in these secret grottos, but strange geometric shapes - some have speculated that this is a proto-language - but I like the idea that they are there to aid the hallucegenic trip. Places started to become sacred.
So now you have the mass of society with naive religious beliefs and a caste of shamen who commune directly with the gods.
Roll forward time: As society developed with the advent of agriculture the nature of the gods and religion changed:
- the people would see death and re-birth in their crops - particuarly in temperate zones with seasons, so the idea of 'vegative' gods dying and returning was transferred across to the Other Realm (see Frasier's 'The Golden Bough') Ultimately this would give rise to Christianity - which pulls off this rebirth feat with a monolithic god which is really quite impressive.
-Societies needed to be organised to be efficient in agriculture and Religion as an organising force was recognised and used (really a secular development, but important). Hence the shamens became priests, even kings - morals were codified and enforced. (although I'd say that the necessity of warfare split this role into two: a spiritual and a secular position. High priest and warrior King so to speak.)
-The inaccessable natural sacred places became temples in the peoples cities, places where only the priests were allowed access and was taboo for the public.
Note though that the great religious prophets/saints/leaders still had to go to extremes to touch the realm of god/the gods - they fasted, self-mutilated, were 'blessed' with epilepsy, lived for years in isolation in the wastes of the planet or even atop a marble columns. It had to cost you to commune with god. Still shamens at heart.
Even in the rational world of science we have this template. Great scientists are deemed special, different from the rest of us, uniquely gifted. They commune with the Other Realm - but in this case this is realm of mathematics, modelling, logic, rational thought, science - and they bring back gifts and messages, explanations of how reality works. It too is a realm deemed difficult for most of us. And it costs, men and women destroyed by their visions: Boltzmann, Godel, Cantor driven to madness and suicide for example...
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Right my essay is getting a bit too long and convoluted, I'll leave it there

Hope you get something from it.