but when you "start a conversation with someone" is that like sending them a private email? I sure hope so cause I don't want to type all that again. The reason I ask is that it no longer appears anywhere though initially it showed that I had a private conversation going. I hope that isn't like a chat room that disappears.
No - it's not really like private email - think of it more as a "private thread". Conversations you are a participant in will be listed here: https://www.zoochat.com/community/conversations/ (you can get here by clicking on the Inbox at the top right). It shouldn't disappear unless you are looking in the wrong spot? Perhaps you are looking at the "unread conversation" list which show when you hover over the Inbox link at the top right of the page? Conversations you have already seen all of won't show up in the unread conversation list drop-down until new replies appear.
PS. I changed the title of the thread to make it more meaningful for people searching for information on this topic in the future!