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Coming from 20+ years in the PC world, I understand how hard the transition to Mac can be.
You want to open second browser window?
Fine, go to the Safari menu bar (top of the screen) and choose "File/New Window".
Or
Command-N for a new window
Or
Right click the Safari Icon on the dock and select, yeah, you guessed it, "New Window".
What is so tough about that?
~gtd