WooCommerce search works only on key-word of a product and our theme does not influence that. If you check on any default theme, StoreFront, for example, you will have the same issue. The only way out is to display your Category navigation in a sidebar or in the main menu.
No, there is no option to remove the text. You can remove the whole Category drop-down and leave search only. For this purpose go to Woomart Header Builder, enter the search element and disable “Show Categories Drop-down” http://prntscr.com/j8616z