You’re looking at doing some custom wp_query filtering! Check out the Custom Field Parameters, this will give you a rundown on how to implement.
I don’t have quite enough time to look into pulling in GET parameters, but here’s a sample of custom field filtering that I have open in front of me. The first one does actually look at the URL for variables, but probably not the proper WP way.
Use an action hook, make sure that you have your URL variable and the right post type, then apply your field filters:
For this example, I’m filtering post type “properties” and doing 2 meta queries: firstly inside a price range (price_min and price_max), and secondly if a location variable has been provided I am filtering on a district_rel custom post relation field.
Let me know if you want a hand adapting this for your date field 😉