You can, of course, add filters to the search, as long as you have a different source of meta data (terms) for each of them. At the moment, you have only a custom taxonomy named categoriesignature
.
You add can custom fields (Post Meta) or other taxonomies.
As to the sidebar question, that is dependent on your theme, or page builder, and this is not something that comes within the scope of our support.
I can see that the form you have currently has some alignment issues with the radio buttons and checkboxes, which may require further custom CSS to align correctly.
In the main, our form is relatively unstyled, leaving it to the user to add their own style using custom CSS in the theme custom CSS panel, or the WordPress Customizer (and there are other methods for importing CSS to a site).