However, this is not something that science can prove, at least without adding the claim that the only facts there are are physical facts. You're basically suggesting that we open up people's heads, look around, go "Nope, no norms here!" and take that to be evidence that they don't exist. This is problematic at best, since were they to exist, normative facts would seem to have properties quite at odds with physical facts, and your assertion starts to look question-begging.
Metaethics is not my area, so I'm afraid all of this is rather rough and ready, but the SEP article [1] is a pretty decent starting point.
My point was that there is nothing science won't be able to prove; and that there is only physical reality, and facts, and that once we crack the 'code' (as in 'security code', not 'programming code', although in another discussion I'd posit that it's both) we will learn about the fundamental nature of morality - as humans perceive it; it's exactly this realization (that moral issues stem from interpretation by man) that will show that most things we consider 'moral issues' really aren't.
(the above may make it seem that I'm a moral relativist but I'm not - au contraire, once we peel away the human-induced layers of morality we will find the fundamental nature of it at the core)
Sure it can. Take north western Europe, notoriously secular (when compared to the US) yes quite socialist with an extensive social safety net. Economics, sociology, etc, all help you identify what you need to do to reach what ever goals you are aiming for.
And ethics and fairness have been studied and are well known in other social species, like the great apes. They are not uniquely human.
Morality is just the formalization of a whole set of instinctive emotional desires for fairness. Most often it is enforced by using another emotional foundation, the respect for alpha leaders, as in it is God's law you do this and that.
There is no domain which will eternally be out of the reach of reason and science, not morality, not love, not spirituality, nothing. I find this wonderful!