1) the html Structure/css of the chat should be in a separate file? How it is then to integrate to the site?
-- How convenient, and done. Usually depends on the volume of code and goals. If you do a simple chat to one site, and General styles to push.
2) are There any requirements for chat? I read somewhere that blocks head and body should not be, as well as because this file will then be added to the ready website.
-- This is nonsense. To get code for chat on website with direct hands and full access to source code – no problem. In other cases, helps iframe.
3) Can throw links in codepen or sample code for such chats.
-- Simple search on the tags 'chat' in codepen gave it