Web-Based Multi-Device Synchronization

I have to build a prototype which consists of various applications for multi-device real-time synchronized functions. This all needs to be implemented on a website so they will work through the web browser, and not native apps.

Some examples are:

• The first case is similar to the Play Store, when you open an app on play store from the browser on your laptop, you chose the device and it installs it on the phone. In my case, it would be that you have found a video on my website, and directly from there, you select to play the video on another device which has the website loaded, and possibly control it.
• You are writing a comment on the website, and before posting it, you switch to another device, and the unfinished comment shows up there too.
• Similar to the Facebook page notifications that show on the edge of the screen, in my case you are browsing an article on my website, and you mark it to read later, and a notification shows up on all devices where the website is open.

For this I guess I need some way to uniquely identify devices and save them, check if they are online (if the website is open on the device), synchronize commands between browsers through the server, save states, etc.

I know I'm asking for a lot, but I need some tips to begin with because I'm not sure what to do. If anyone can point me in the right direction, what tools, frameworks, etc. I would be really grateful. Last but not least, the website on which I have to add these features is based on WordPress, so if there is any add-on or anything that would help me with that, please tell me.

Big thanks to anyone that takes the time to answer.