No, humans have built all this stuff because it provides value to more and more people. Time spent on status games is time not spent doing something productive.
Possibly, yes.
> which is why people care about it
No, people care about it because it produces valuable things. People would still care about productivity even if nobody had the slightest idea what status was.
No, they care about them because they need them. People need food, clothing, shelter, companionship, and many other things. People also provide those things. Producing those things and trading for them is not "status"; it's filling genuine needs.