I created a new theme, starting by zero. The theme works correctly, but some plugins not.
I installed Google Analytics & Webmaster Tools, I compiled the plugin with my track codes, but in the html code them did non appear.
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By the sounds of it, your custom theme is missing the common hooks that allow plugins to alter/output their code.
Here's a real-life example. The WordPress Twentyfifteen theme has this in its header.php file (traditionally the part of a theme that outputs the section of any page):
... other <head> stuff wp_head(); wp_footer(); ?> </head>