Привет is even less formal, you should only use it with close friends and family.
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.
Not if they're younger, the same age, a long lost relative, one of your twin daughters that you can't distinguish, etc.
Здравствуй is informal, use it if you would address the person as ты. If you need to speak formally (using вы) Здравствуйте is the correct form
"Hello, you're Vera?" was considered incorrect? Perhaps it's not entirely natural sounding in English, but I should think this is still a correct translation, no?
Not natural, because not grammatically correct. "Are you" is the correct order.
"Hello, you're Vera?" can work in English; it just connotes differently than "Hello, are you Vera?" "You're Vera?" suggests you expect the answer is "Yes.". "Are you Vera?" carries no prejudice towards "yes" or "no".
I believe that "Hello, you are Vera?" while not overly common, should be considered correct. Especially because if one hovers over ты, it shows "you (are)" as one of the options.
This phrase is wrong. If it is a formal phrase it should be "вы" and not "ты"
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.
My French-Russian textbooks taught me that "здраствуи or здавствуите mean good morning or good day. Are they wrong?