Chat - message - faq module for existing website in php from scratch

I have a responsive web application in php. I need to implement from scratch a chat - message - mail module for the existing website (php). I want this module to implemented separately and then my developers will integrated it to the existing website. The module has automated and non automated part. Visitor or user see a chat box with an automated question list and select between them. These questions lead to another question set or to support articles or to send messages to the corresponding with the topic, department. So we need a cms in which will set the automatic question by user type, the relations between questions and the actions will be done by user selections. After that we need a chat box and a chat page in which user can manage his conversations. The chat page will be organised in 3 regions: conversations (instant messages), mails (non instant messages) todolist (pending from other users)