@Ashoulder2leanon If a member quits responding, I think it is unlikely they will give you a review when they return, but it's possible.
Yes, a listener can end the chat by pressing the End Live Chat button near the top right. I believe the member will then be invited to give you a review, but they might choose not to. You have no way to tell whether they do or not.
I think it's OK to ask a member to give you a review just before you end the chat (but I'm not sure where I read this). If the member knows that reviews are important to you, this might make it more likely they will give you a review. I don't ask members that myself, so I don't know how well it works.
Charlie