How to remove all the divs inside the $widget of a views exposed filter?
Go to the modules directory and look for the 'views' module.

There is a 'theme' folder within this. 

In the theme folder, copy the 'views-exposed-form.tpl.php' file to your theme.

You can then edit the template as you require.

Note, when you copy a file like this you will want to clear caches for this to work.

*****UPDATE*****

To edit specific components of the form I suggest you override the following function in your themes template.php file.

template_preprocess_views_exposed_form(&amp;$vars)


This can also be found in the views module folder 'theme.inc'.