I leave Firefox and Thunderbird running full time. On a reasonably
modern computer this does not really effect the machines performance.

Gnome desktops all run the one wallpaper that you have chosen for the
machine. KDE used to allow the user to choose a different wallpaper for
each desktop. It's been a long time since I've used KDE. I can not say
if it still allows different wallpapers for each desktop.