Create new or modify existing WordPress user messaging/interaction plugin/module with triggered actions -- 2

I need a module/plugin on a WordPress site where registered Users can communicate with each other via a strictly defined and given way (by design) and also kind of interact. For example a user on the website is offering a service (a little bit compared to freelancer here) and I want to take advantage of that offer. I have a button where I can contact that user and discuss things about the service he offers. At this point user information is on both sides is hidden. When the user who offers the service thinks "okay, let's do this" he clicks on a button and this button should trigger that both participants of that "chat" receive an e-mail AND a personal message on the website in their Inbox with all the (predefined) user information like last name, mail address and so on. So I would also need a nice looking (should fit to the rest of the website design) messaging platform where every user has an overview of all his conversations with other users. I will attach some ideas that I quickly noted in Word (sorry for that) how the process should look like. The website is in German, all my information I provide is in English for better understandings. I will take care of the translation after the project is finished. I am looking forward to work with you!