Selectbox and Searchform and Custom Search Page

Welcome to WPSE!

First of all – you cannot have two (or more) elements with the same ID. Second – your select elements lack name attribute and browser doesn’t actually submit anything. Third – you cannot just expect to throw a bunch of selects into the form and expect everything to magically work. In order to even start searching, WordPress needs a query with s key – only then it will recognise the request as search and redirect to the appropriate search template.

As I said before, building a complex search system is not an easy task. You will probably need to hook into a pre_get_posts action, detect if certain values have been submitted and modify the query accordingly. Here’s an article on how to build advanced queries using WP_Query class to get you started.