I believe intparent was referring to the school that ZM previously applied to, not the DA. But Kriston is right, the DA is a free public school, not a private school. Keep in mind, though, that there may be costs involved for DA students taking college classes, if that's the level your child is working at. Tuition/books for classes that are required for high school graduation are covered by the DA, even if they are UNR or TMCC classes (which a student would be taking for dual enrollment). That said, there are some necessary restrictions. If a class is given at the DA, and a student decides to take a similar class at UNR, that tuition is coming out of the family's pocket (which makes sense). Classes that aren't required for high school graduation are also a family responsibility.
As for age, that is much-discussed topic among current parents. There have been DA students admitted as young as 9, but I really can't speak as to their success or difficulties with the program. I can tell you that the older students act and talk like high school-age students, and the subject matter of their conversations and the vocabulary they use is typical of teens today. Many students are also in relationships. Gifted teens are still teens, and the risk-taking, defiance, and generally annoying behavior so prominent among teens is alive and well at the DA (my own kid, included).
While younger/older students don't tend to socialize much, a certain amount of overlapping is unavoidable in such a small school (especially one at which ability-grouping is the norm). Young kids are going to see and hear the older kids -- in class, at lunch, on the shuttle bus -- there's no avoiding it. Basically, if you wouldn't want your younger child in a high school environment, I would think hard about the DA (or any school with older students). Most DA parents I know with younger siblings choose to wait until typical middle school age to enroll their second child -- even if they academically qualify for the DA at a younger age. If I had more younger children, I wouldn't dream of sending them to the Academy until they were at least 11 or 12. I, though, tend to want to extend the innocence of childhood as long as possible for mine, others may feel differently and I don't mean to imply that another point-of-view isn't justified as well. Everyone knows their own kid best, so it is an extremely personal decision. I'm just giving my opinion as someone who has been there, I certainly don't mean to say there's one right age for admissions. Nothing is that cut-and-dry with these kids!