The Advanced Woo Search plugin will work great without any additional settings with almost all WordPress themes.
By default, the plugin does not add its form automatically. You need to add it in one of the ways described above.
This setting does not work for all themes. Please try other described ways to add a search form to the website.
All depends on the WordPress theme that you are using and the place where you want to add the form. If you are not familiar with coding it is better to contact the author of the theme or with a developer that can help you.
Plugin doesn’t create its own search results page layout. It just adds its search results to the existing layout of your theme. So if you want to customize this page, use your current WordPress theme settings or page builder plugins to do so.
Yes, sure. There are special settings for this. Please read more here.
Download free version from wordpress.org repository.
Read about differences between free and pro versions here.