Giuliani clearly did know about the letter, you could tell he was just dying to reveal more when he was asked about it like a gleeful child trying to keep a secret. He has a lot of connections to FBI agents so I'm not at all surprised he would have heard something about it. That doesn't mean the FBI purposefully leaked something, it means some agent(s) blabbed to him about it.
I don't have a clue what the meeting between Lynch and Clinton was about, but it damned sure was not a friendly chit chat about grandchildren. It was inappropriate, but I doubt it had any bearing on what happened with the investigation. If I had to bet, I'd bet that it was Clinton basically telling her: "hey, level with me, we're in private and nobody will know, what's going to happen with this stuff?", but that's just baseless speculation on my part.