Krishna discussed Karna's birth with him when leaving Hastinapura; all the followers were asked to go back to the city and only Karna continued on Krishna's chariot. Interestingly this conversation was narrated by Sanjaya to Dhritarastra (Sanskrit, translation).
In that conversation, Karna says he knows about his birth.
I know all that thou hast said unto me.
I have many questions here.
How did Sanjaya came to know about this when the conversation told place in private. At that time Sanjaya did not have the devine sight
After knowing about Karma's birth, why didn't Dhritarastra act? Did other Kaurava's (Duryodana for example) heard this narration from Sanjaya (because Dhritarastra asked Sanjaya to narrate when Kauravas were discussing about the peace deal)?
How did Karna know about his birth before Krishna said it to him?