When using two monitor the panel allows application to go under it. You must go to Panel Settings -> More Settings... and select Always Visible in order to restore it. Is there an option I am missing that prevents this behavior? Is it a bug?

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How often do you need to restore the behavior? Presumably it should save the setting when you log out (or close the desktop). It sounds like it isn't saving the setting (possibly due to a crash on logout or other premature exit?)

I must restore he setting every time I connect a second monitor.

I also noticed that some times trying to maximize a window on the main screen (smaller one) will cause the window to move (maximized) to the secondary monitor.

Hmm.. that's outside the realm of my experience (static dual monitor setup). You might search around for the various threads about Multi-monitor setup to see what others have run into, otherwise I hope someone who has more experience with multi-monitor setups can come and assist.