Hi Celia

Ok so there are two main issues.

1) Display problems with the search form controls.

Your theme actually has some CSS that hides the checkboxes/radios and also hides any submit button in the sidebar.

This means any plugin that adds a submit button or a radio button into your sidebar will not work without modification.

I’ve identified the code for the form controls which is causing you issues (in base.css):

a, input, select, textarea {
    vertical-align: top;
    outline: none !important;
    -webkit-appearance: none;
    -webkit-border-radius: 0;
}

Its the -webkit-appearance: none; that needs to be disabled, or overwritten – your theme should not be applying this kind of rule globally to your website.

You also have

.sidepanel input[type=submit] {
    display: none;
}

Which means any submit button in the sidebar is hidden. 0

2) When you submit the search form you get taken to another page without the search form on it.

Well, you need to actually add the search form to the search results page. It looks like you are using archive display method – http://www.designsandcode.com/documentation/search-filter-pro/search-results/as-an-archive/

You must edit the template you have specified and add the search form somewhere to this page using the shortcode, or you should add a sidebar to the page and use the widget:

http://www.designsandcode.com/documentation/search-filter-pro/getting-started/display-search-form/

Thanks