The best answer to this question is that morality and society are the result of evolution, and as such are likely to be beneficial to the fitness of the species. To be more precise about that, if there was ever a divergence where ancestors differed in their morality or their society, the versions of these complex phenotypic effects that were most beneficial to fitness would have survived.
This is not as simple as I suggest, but it is certainly true about any genes that are related to the development of this phenomena (in other species as well as in humans - the societies of ants and bees are in some ways more highly evolved than ours, with their specialised epigenetically differentiated variants.
I would say yes. If we evolved from monkeys and are just part of a natural process then why have morals at all? I mean lots of animals eat there babies and eat each other so what makes us better? This has nothing to do with whether evolution is true or not, it's just to talk about what it would mean for our moral systems if it was.
There is an entire branch of science called "Evolutionary Psychology."
We can look to Nature, and often find acts of morality, or even altruism.
A wolf will bring a small kill back to its pack, to share with the pups.
I have seen a cat risk its life, to draw of a pack of pit bulls attacking an old lady.
And a bee will not think twice about laying down it's life, to defend its hive.
hundreds of examples like this, go to answer "why do?"
If your question is more "why should?" then there is an answer for that as well.
Because there is nothing in Evolution which precludes a Heaven. Or a Hell.
If fact, some say Evolution literally requires such things.