Approaching it from an idealistic perspective, in order of your questions: Yes, this should be part of both law (directly or indirectly), and the social contract.
From a more down-to-earth perspective: None, and yes. People care for - and this changes dramatically depending on one's personal circumstances and prevailing culture / zeitgeist - in a general order:
- Their security and happiness
- Their family's security and happiness
- Their friends' security and happiness
- Everyone else's security and happiness
There are, of course, exceptions (and is probably the only way we actually have progressed as far as we have!), but generally - "I will only feel responsibility for those I care about, and I have enough left in me, then maybe other people." It's how we are wired, and it can easily be taken advantage of.