Create a custom search results page based on mockup (plus couple other tweaks)

You can take a look at the website at [login to view URL] There are three components to this project. Firstly, I have attached a mockup demonstrating the work I need done on the custom search results page. Secondly, I need the Relevanssi plugin installed. This will replace the WP search. When activated, the live search bar you can see at the top of the website stops working. It should be a simple fix, but you'll need to ensure the search bar is working correctly with the Relevanssi plugin. Thirdly, there is a relatively minor fix needed to get a custom content type to show up on a category page. By this I mean there is a custom content type categorized as "Books and Literature" which doesn't display on the Books and Literature category page.