Does Arch Linux we download from their website comes with a desktop environment ? If yes, which one ? Is it possible to use it as Live CD to see whether it is useable ?
As far as I know there is no live image of Arch, it must be installed. It’s been awhile but if I remember right you can choose from several available DE’s durning the install. If you are unfamiliar withe arch way you will need to follow the install guide very closely. You may want to try Manjaro first as it has live versions and you can download the DE of your choice to try.
I tried Arch a few years ago and I installed KDE and it worked great.
Don’t know if this will help, I found it yesterday as I was looking at Arch as it not something I know a great deal about: https://www.slant.co/topics/14976/~desktop-environments-for-arch-linux