BTW, what does the star after someone's account here mean?

You get a outline star when you get to 1000 points.

Members with a solid star have moderator privileges  

Either mod...Example CPhill....Site Operator.....Admin.....or Power User....Alan

How you become these?  I don't know.......

And, so, how do you get these fable 1000 points of yore?

Sorry, not fable, "fabled"

You get points by asking good questions and by answering questions well.