I am sorry, I do not understand. Could you provide me with a far more detailed description of the issue? Have you already made a form, and if so, are you able to send me a live link/URL to your search page so I can take a look?
What do you mean when you say ‘input from a custom query’? Have you created a wp_query with arguments that you want to use, in a template file? If so, what are those arguments and are you able to share that template with me? To the values in the wp_query change or are they fixed?
Do you need a results page with a fixed URL, or does it want to be on the theme search results page?
Do your results need a specific format that already exists in the theme/site, if so, can you provide me an example of the look an feel of that layout on a current page in your site (i.e. not an example from a different site)?