I'm pretty sure Twink was made an honorary Star Spirit at the end of Paper Mario, so I imagine that it takes a certain amount of guts for a Star Kid to eventually become a Star Spirit. Since all of the Star Spirits appear to be different ages, there probably is some sort of succession going on there, though whether or not there can only be seven at a time is a mystery to me.
Geno specifically said that the Star Pieces are literally the pieces of the Star Road. How the Star Road is connected to Star Haven is another mystery, but my theory is that it's an actual road that connects Star Haven with other areas in the cosmos. Also, those little star-shaped thingies that connect Star World with the regular world in SMW are also called Star Roads, but I doubt there's a connection there.
The Lumas don't look to be related to Star Spirits outside of being star-shaped. One heavily resembles a Starman and exists soley to grant wishes, while the other looks more like a marshmallow and literally an infant galaxy/planet/comet/star/sun other celestial body.
The "higher authority" Geno was talking about was probably the Star Spirits, since Paper Mario establishes that they're essentially the top of the wish-granting heap. Since they're all wise and such, there's a good chance they know who Rosalina is, and since Rosalina pretty much created the universe, she probably knows about them.