how can I do override the default WooCommerce products search form on my custom WooTheme ?
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Exists the template
product-searchform.php, you have to override it in your theme.
More information here about how to override WooCommerce templates from your theme.
Basically the WooCommerce search forms returns only products and not also other post types because the product post type is specified in an hidden input:
<input type="hidden" name="post_type" value="product" />