Is it wajib for one to do silat ar Rahm with his cousins too? What if a cousin never reaches out to you, and has adopted kufr practices and no longer looks like a Muslim?

Yes it’s wajib to reach out to family members including cousins. You should still try to reach out to them and do Amr bil Maroof in a very diplomatic way. Unless if they choose to ignore your advise. In that case no need to insist