ubuntu: position of menu icon on the top menubar changes randomly

"You can try enabling Locked Down mode. This should prevent any changes to the panels until you modify the key again.

Press Alt + F2 and run gconf-editor
In the left pane, expand to apps -> panel -> global
Enable the Locked_Down key.

If you enjoy a command-line approach, this is how you can save and import gconf settings:

Run gconftool-2 --dump /apps/panel > ~/settings/saved_panel_settings.entries to save your panel settings
Run gconftool-2 --load ~/settings/saved_panel_settings.entries to reload them
Run killall gnome-panel to restart GNOME with your loaded settings

For an easy way to switch between layouts and save layouts, check out PanelSwitcher."

"Q2.
See if you have Expand option set in panel properties. if not, then set it and check if the icons are moving.
Also I dont have any icons locked but they retain their place. Unlock all the items in the panel and see if they move around."