It's not that it's unusual, it's just that similar behavior is also an abusive tactic called love bombing. Imo, I think the kid is just being a bit awkward, but that doesn't mean this behavior isn't a problem. Like you said, it's (probably) just teenagers being teenagers, but I don't see anything wrong with pointing out how this can be a problem.

Like most situations, the best thing OP and friend can do is have a candid conversation about how they're feeling towards one another and figure out what they're both looking to get out of a relationship. Having been 19 myself, I doubt that conversation will happen in a way that is "correct", but at the very least she now knows that love bombing is a thing and that it's important to think about your own safety, wants, and needs