Is it possible to add Chromecast to the CX-5 screen?

I understand that ideally it should work ONLY when car is stopped.

 

Welcome to the forum

 

I don't see how it would be possible. Maybe you could somehow add it to an aftermarket stereo, but even then it would still need to be paired to Wi-Fi...

 

Never even attempt such a thing, in fact, get it right out of your mind.
It's an accident just waiting happen.
If you got kids and they want to watch something from the back seat, get a portable player.
With a cord that will not reach the front seats or the dash.