No, unless you are doing a group chat (if that's even possible; some programs don't support it). Typical IM (instant messaging) applications use one-on-one chat windows.
Everyone can see your status (online, busy, etc), unless you change it to "invisible" or "appear offline"; you are still online, you will still chat with those who know you're online, but you will appear logged off to everyone else -- and yes, you can see other statuses even when you're invisible, unless they are invisible too. ;-)