why is "здравствуй, я здесь" wrong?
It should be accepted, report it. "Здравствуй" is currently not very common, though. When you are on "ты"-terms with someone, you are more likely to say "привет". However, adults often say "Здравствуй!" to a child, replying to their "Здравствуйте!"
I would never translate Hello as Privet. Privet is Hi.
I hate the russains
If this were a phone conversation I would even say алло instead of привет