for the action label, there are some reserved terms, that wordpress uses internally. so you should avoid this terms (specially true in http_post ot get requests). ‘s’ stands for search, that’s why the output is a search result page. here you can find reserved terms: https://codex.wordpress.org/Reserved_Terms
If you need very simple forms (so it seems in this case), i would suggest you to learn how to append variables to an url with add_query_arg. Here’s a good place to start, it’s quite simple and ready to use : https://developer.wordpress.org/reference/functions/add_query_arg/