There are a few ways using VNC servers and clients. Though the utmost easiest remote desktop solution without any real setup is TeamViewer. https://www.teamviewer.com/en/download/linux/
As for using this as a OS on another monitor. Well you're not going to have an amazing experience if you're looking for something hardware accelerated. There will be input lag and/or basic graphics so playing games and stuff is out of the question. If you want to go full graphics support you will need something like KVM + QEMU to VGA/PCI passthrough with a second graphics card. Otherwise you're going to just need to do it the old fashion way, with another PC as the host of the OS.