I would be alright with Khaji knowing about Terezi's biological makeup (him being a troll, how his blood color affects his lifespan, how he's blind and his other senses compensate for it, etc.). His powers would probably come out as vague white noise or "he can see the future" without too many details, though. His powers came from a force more powerful than Gods, so it would be reasonable for him to not know too many details about it, I think.