We recently added chat search; it works much in the way you described though you cannot search specifically by date.
Take a look at this topic and feel free to suggest improvements once you’ve tried it out! Introducing chat search
Right now, anyone in the group chat can add members (until they reach the limit of users who can be in a single group chat, based on the chat max direct message users setting). So is that not working out well for you, and you want to prevent chat members from adding others?
(You’re correct that members can only leave of their own accord; we haven’t built the ability to remove folks from the group chat.)