It doesn't deny the importance of family and community. It stresses a need for self-worth and productiveness so that one may participate in a meaningful and fulfilling manner.
That's putting a new gloss on Ayn Rand if ever I heard one. Things like taxes and wealth redistribution only serve to help people "participate in a meaningful and fulfilling manner." If Objectivists are so interested in community, they sure don't act like it.
We won't know because it doesn't exist, and most likely won't any time in the near future. It is our current manner of living that cannot be sustained.
What we
do know is that all systems wind down. Nothing can last forever, and it is naive to think that an unregulated market would somehow not be subject to the laws of physics. This is one of my major problems with objectivism and libertarianism in general, is this assumption that the free market is some sort of transcendent principle. It is just a description of how economies behave, and economies are made up of people. People are more important than pennies.
Of course it's perfectly natural for us to care for others, but in order to care, one needs to be mentally, emotionally, and financially capable of caring for others.
I'd like to see your evidence for the assertion that "in order to care, one needs to be... financially capable of caring for others." But aside from that, how exactly does this support objectivism? Egalitarian and communitarian philosophies do not oppose people being mentally, emotionally and financially able to care for others, indeed they encourage it, particularly with regard to ensuring the financial capability of every person to survive. Objectivists seem to be more concerned with allowing people the "freedom to starve" than with ensuring their ability to survive and care for their families. In short, the above sentence functions more as an argument against Objectivism than in favor of it.
Why is it nonsense? The natural order of importance in most peoples' list of priorities is self/family, community, state, nation, world. If you don't exist, you cannot provide care for anyone. Would I give my life for my family or someone I loved personally? Yes. Would I give my life for someone I don't know? Maybe.
It is nonsense because it needlessly contorts the idea of selfishness and altruism, which I will address below.
Pretend to be altruistic all you want, but there's no such thing. There are varying degrees of selfishness, of course. But selfishness is always there. Simple fact.
A simple fact, indeed, rivrrat. One might even call it simplistic.
What you dismiss as "varying degrees of selfishness" is the very difference between selfishness and selflessness, the difference between morally reprehensible and morally praiseworthy... to be blunt, those "degrees" are the difference between evil and good.
I've read Heinlein too, he's a great SF writer, but he was also a crotchety and selfish old man, and his brute cynicism is illustrated in his idea that a saint is just as "selfish" as someone who dedicates his life to pursuit of material wealth. This is sheer sophistry. When a saint, like Mother Teresa, dedicates his or her life to the assisting others, the saint is doing something good, that is beneficial to others, and the self-interested good feeling one gets from altruism does not detract from the praiseworthiness of the action. Perhaps if you remove that good feeling, the saint may not pursue the good ends, but this does not make the pursuit of goodness "selfish," merely self-interested, and in a way that does not come at the expense of others. Contrast this with somebody like Gordon Gecko, whose ruthless pursuit of material gain is "self-interested" indeed, but is also what we would call "selfish" because the good feeling he gets from his pursuit is at the expense of others, he sacrifices the needs of others to achieve this good feeling. This sort of self interested behavior is
objectively different from the selfless (if self-interested) actions of the saint.