#5 could be Ender's Game, except the Battle School was in Earth orbit (and then he went to a base inside an asteroid). But at least it's a better guess than my previous ones ^_^. I know it's wrong, however, because you've said #6 was by far the more popular work, and well there are certainly works more popular than Ender's Game, I'm hard pressed to think of one one far more popular, at least within SF/fantasy circles.

(Scalzi, btw)

(Google feels like cheating, and is doubtful in is efficacy, but I now believe I have not read the books referred to by #5 and #6.)