I have watched every single KA episode, and Kavya knowing that Shlok was his half-bro was never established.
I really don't think so; unless you can point me to the specific episode.
Nitya only told Kavya that he was Pallavi and Mayank's son. She never went on to tell him that Shlok was her son. Even Shlok and Anjali never told him this.
All of a sudden, Kavya knows that Shlok was born to Mayank and Nitya and given to Vanschita to raise.
C'mon.