"Do you know him?"
Translation:Ти знаєш його?
I can't speak for Ukrainian, but I'm fluent in Russian. Because of verb endings, my guess is that ти is optional. So you could even say "Його знаєш?" and it would be fine. In fact when i speak with native Russian speakers, that's the preferred conversational way to say it.
This would translate to:
Do you know? Yeah, I know.
Very conversational. Fewer words.