Is it possible to create a "newsletter form" and add it as a widget to the side bar?

Dear Gerrit,

You can read how to use shortcodes in sidebar. The same code should work for other parts of the template too.

www.wprecipes.com/how-to-add-shortcodes-in-sidebar-widgets

Also follow this link to find out how to add a shortcode of Spider Form Maker.

web-dorado.com/wordpress-form-maker-guide-4.html

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Best regards
Web-Dorado team