Intigrate my Chrome Extension With my Wordpress Website & let user auth login into third party account woithout password

Hey, I'm working on a proxy & auto login based Chrome extension. I want two things from extensions, 1. First user login to my WordPress website and then cookies should be set on his chrome browser if he removes my extension or log out from my WordPress site then my third party account automatically log out. 1: User can access my paid account without password like mail.com. I'll list account logo on my website, and when they click on the logo, a separate tab should be open like this **[login to view URL]**. When they click on another company account every part of URL should be same except **FB** replace with account name Which I give like [login to view URL]**gmail**?=5555 2: Account must be automatically log in from my assigned IP only. which is possible with findproxyforurl function. I'll provide you my extenions source code. You just need to integrate it with my wordpress website & let user auto login to my third party account. Basically I've codded al most everything I just have trouble in third party authorization. Keep in mind I can't use thir API.