Is it possible to logout to any other DE without close any running application?

You can open n sessions with the same user :

you could install Xephyr o Xnest(older) and then open a new Xsession in a window (like a Picture In Picture):

startx /usr/bin/startkde -- /usr/bin/Xephyr :2

startx /usr/bin/gnome-session -- /usr/bin/Xephyr :2

or CTRL-ALT-F1, login and open a new X-window session:

starx /usr/bin/gnome-session -- :2 or any other session manager or command, ie xterm

And move between sessions with CTRL-ALT-F7,F8 Just beware of RAM :)

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