Message history via email

Hello, I have two problems:

Every time you visit our website where the chat is opened, a chat is also opened in the mailbox, although the visitor does not write a message. It quickly becomes very confusing. Can you set this so that this only happens when the user writes something?
How do you get informed about a message? We cannot check the page manually 24/7. An app etc. would be good.
Or by email. Here I am unable to send the entire process directly by email. I can only send individual answers by email. How is that possible?

Thank you and best regards