You also might have a chat with the kids about how mom and dad are living separately now, and that unless there's something one of you NEEDS to know about what's happening at the other house, it's best for them not to be carrying reports back and forth.
You can explain that adults have a right to privacy. You don't want him knowing all of your business, and he doesn't care to have you knowing all about his. You want to STRESS that if they feel scared or uncomfortable about something going on at one house that they SHOULD tell you (or their dad, if it happened at your house), or someone like a teacher or counselor at school. But that just everyday stuff--what they did on vacation, how much money someone makes, whom someone is spending time with--those things don't need to be shared with the other parent.
It's good to have a conversation like this. After all, you don't want the kids talking about whom you're seeing, etc. And it will spare you from hearing some of the details about their lives.
Incidentally, blocking them on FB is a very good idea.