AFAIK a task can only be used from the desktop in which it 'resides', tasks can be moved between desktops via drag and drop.
Task Manager shows all tasks irrespective of which desktop they are on, but without any indication of which desktop they are on
You can use the Task Manager context menu to switch to tasks - if they are on another desktop it will 'push' the current desktop aside.
Different desktops cannot have different wallpapers (nor can they be named)
There's a gadget at CP that claims it can do it, it's on my list of things to try as its the thing I miss most from my old VD manager.
Added : Oh yes, use Win+Tab to see Desktops, you don't need the Taskview icon cluttering up your taskbar. Also Win+Ctrl+→ and Win+Ctrl+← will traverse VDs.
BR