I don't know about Russia, but in Czechia we address 12 year olds using "ty" (the informal you). "Vy" becomes the norm around adulthood (18 years). Some much older people use "ty" even when talking to youngsters in their 20s or 30s, but that's already a little rude or condescending.
Besides the age requirement, "ty" is simply used among friends and family, while "vy" is used with anyone else - neighbors, shop assistants, people on a tram etc. The line is blurred with colleagues at work - it often depends on the company policy. But usually you begin with "vy" and once you get a little closer, you switch to "ty". The older person should be the one to suggest using "ty". If both are approx. the same age, then the woman makes the call. In case they're both the same age AND same sex, it can be whoever is bolder. :) Sometimes the switch to "ty" never happens - when the two people want to maintain a strictly professional relationship or they want to keep distance between each other.
The word definitions are not based on age.
ty = you singular informal/familiar vy = you plural formal & informal/familiar vy = you singular formal only
Now, whether or not you'd use the formal form is based on age (among other things). So, kids use the familiar form when talking to each other. Parents would use the familiar form as well when talking to kids. Kids would use the formal form to talk to adults outside their family - e.g., teachers.
As a kid, it always seemed to me like adults addressing 13 year olds using the formal form as "silly" and "awkward". Now that I think about it, it sounds like a good way to slowly transition the kids from being on the bottom of the social ladder with respect of the formal you to adults!
From what I remember, it started by "young man" and at some point the "young" got dropped.
Pronouns (as subjects) can usually be left out in Czech. But not in this sentence, because they form a contrast with each other here. Think of is as "You are girls, whereas we are boys." In fact, we could omit the second verb, but not the pronouns: "Vy jste holky a my kluci". In the separate individual sentences, it would be possible to omit the pronouns: "Jste holky." "Jsme kluci." - but even here, depending on context, it sounds more natural to include them.
Pronouns must be present in all such contrasting sentences. E.g.: "Já piju pivo a ty (piješ) víno." (I drink beer and you drink wine.) or "On chce jít ven, ale ona ne." (He wants to go out but she doesn't.)