Thanks To
Jazdot
I fixed that issue within the "Displays"-settings: Menu -> Preferences -> Displays, choose the display you want to use as second screen, switch slider to "OFF", click APPLY. Taskbar and everything will (of course) move to first screen. Now you can switch the slider for second screen back to "ON". Taskbar and icons will stay on first monitor, at least they did on my computer.
I Managed to have Dual screen working as it should and icons on the proper screen I wanted.
(I've got mint 13 x64 in a Hp Laptop and as second screen a dell)Here goes a description to help others in need

:
Problem - Dual displays would crash cinnamon ( and no windows properties - aka the title bar, close,minimize area disappears when connecting to the second screen, and rebooting and re-login gave me a screen without the cinnamon bar.
How I solved It: so to have it working I disconnected the laptop from the 2nd screen. , rebooted , and went to the Display Settings and connected once again the 2nd display back (
crash - the title disappears and cinnamon bar gone) but since the window was open I managed to put on Mirror Displays setting.
Logout and Relogin to have the cinnamon bar(I've had a terminal opened for this;)).
Opened again the Display Settings, removed the Mirror Display options, and TURNED off the LAPTOP screen ( btw it cashed again the Windows title area and Cinnamon bar).
Re-login again ( it's repetitive I know

- but now the 2nd Display is OK with - bar and windows title area...
Display settings again - and I activated the laptop display - AND MIRACLE;) ---- I 've got the Cinnamon BAR and the Windows Title Area DIDN'T Crash !!!!!!!( it kept the cinnamon bar on the second Display).
to Be sure....- what else

) - logout and login again - and all was there. Final test Was to disconnect second screen - and the laptop screen flickered but the Bar was as it should; and Reconnected back the second screen - and YES --- ALL OK!!!!
So Once AGAIN - MANY THANKS
Jazdot for your tip !!!!