Hi, How can I use a second screen - high quality - on my portable PC to show the progress of my work while keeping the tools on the base screen?
That is not a function of Photoshop or Elements, but rather of your computer hardware and operating system. If your 'portable' PC was bought in recent years, then it will probably have an HDMI socket that looks like this
If older, then it might have a VGA socket (the blue one)
Or if in between, possibly a DVI port
You need to match one of these sockets to whatever you have on the external display.
To link up is a function of the OS. If Windows 7 or 8, then 'Windows key p' will open a panel from which you should select Extend. After that you simply drag and resize panels to your taste, and when happy, save it as a new Workspace. I don't know how to do that with Elements. (This is the Photoshop forum)