Здравствуй is still pretty formal. Usually you just use привет if you are on ты terms with the person. Здравствуй however is a good way to greet a child in a formal situation, since you pretty much always use ты when speaking to a child, but sometimes it's nesessary to point out the distance. Like when a teacher is talking to a student.
A comment above seems to indicate 3 levels of formality. -Привет is for close friends and family -Здравствуй is for people you know, but not super close with (perhaps coworkers, classmates, etc, that you wouldn't really consider in your inner circle), but still on Ты level with -Здравствуйте is for people you don't know, or just Вы level with
Hope that makes sense
That sentence is on the first view a bit strange. You don't use a formal greating to a person and then you go on informal. (вы <=> ты). But on second view you can understand that sentence this way: first greeting a group, then asking one person of that group about her name.