Are you sure the groups still exist? I presume you've checked the list of groups at the bottom of your info page, but try searching for them on Facebook. One or two of mine have disappeared from my page, but that's because they don't exist any more, or in one case, the organiser of the group switched it to being a "fan" thing rather than group memberships.
Chats - I don't think you can chat to anyone you're not facebook friends with, can you? You can send messages, though, as long as they haven't blocked messages from non-friends.