Hi,
1. Go in the Joomla modules manager and edit the "HikaShop filters module". There, in the menu item id setting you can enter the id of the menu item you want to use to display the results.
Note that by default that menu item must be configured to display all your products.
The menu in which you set the menu item doesn't matter. In fact, unless you need a menu item displaying all your products, you probably want to have in HikaShop default menus so that it doesn't appear as a menu item of your website main menu.
2. In the settings of the filter you have a title position setting. If you select "inside" then you won't have the title and it will actually be added as a placeholder to the input field. So it could be a good way to remove it from next to the input field. Otherwise, yes, you would have to use CSS to hide the title of the filter.