I know that evolution is a change in response to the environment. But shouldn't species have evolved over the years to survive in the natural conditions of other planets and satellites like the Moon as well(without water,oxygen etc.).
Before a biosystem can begin to evolve it needs to start. And while the startup process is probably related to evolution it is not exactly the same thing. Chemical precursors may undergo some form of replication and selection, but it probably begins as more of a chemical process involving some type of naturally occurring bridging mechanism which exists in the environment (clay being one possible example).
And there are other considerations to your question. Life as we know it requires water and a very specific collection of compounds, but we don't yet know the full range of what is possible for "life". SciFi writers have explored just about every extravagant form of life imaginable, but while almost anything is possible, we have no other examples to go by other than our own form of biology.
In general though, I would speculate that the highest probability for life to form would be in "medium" environments which are not too simple and stable and also not too complex and dynamic.
Our moon for example is a very simple and stable environment so there isn't much to work with. While other environments may be too harsh and change too rapidly for any chemical process to take hold.
Planets and some moons (larger than ours so that they can retain an atmosphere and are almost like planets) however have a nice balance of complex chemicals available for accidental associations, and they are dynamic enough to allow for variation and selection to have an effect.
I suspect that there is no life on our moon. But I would put the odds of life on Mars or Europa or Titan or Enceladus at 50% (just my humble opinion/guess). I also wouldn't expect to find anything fancy on any of those places, probably something more like bacteria. But if something does exist it would be incredibly important to learn what it was made of (DNA or something else).
I hope I live long enough to get some answers.