About Chat API Features and Issues

I am currently exploring the capabilities of your Chat API, as detailed in your documentation here. I have a couple of queries that I hope you can assist me with:

Chat Widget Unread Message Display and Disabling: Does the Chat API's widget support displaying the count of unread messages? Additionally, I have attempted to disable or close this floating widget on my interface, but have been unable to do so. Could you please guide me on how to effectively hide or disable this floating chat window?

Chat History Retention: Under what circumstances are chat histories cleared? I've noticed that sometimes, even after a chat ends (chatend), the chat history remains visible. Could you please provide more information on how chat histories are managed and the conditions under which they are preserved or deleted?