Raspberry pi OS under docker

I am using homeassistant supervised on a Raspberry pi 4. I basically use the pi for homeassistant. But as I also use the same pi for internet browsing and other purposes, I have this question.

Can I use Home assistant OS as the primary OS on the pi4 and install Raspberry pi OS on docker. This way I can shutdown the docker pi os when not required.

Can the docker pi os gui be used on the pi with keyboard and mouse or I need to use it as a VNC terminal.

That would be a “Pi OS addon”.
All addons are actually docker containers.

I doubt that exists, but you can look for it.