Hi,
1. I’m afraid that is a theme related issue, the plugin only passes the items there. To make modifications to those, you will have to make changes in the theme template files.
2. Sure, you can do that by increasing the width and the max-height values here: https://i.imgur.com/TRw2q4O.png
3. That is also a theme related issue, the plugin only sends the results there to display.
4. Also theme related. The php version of the plugin shortcode should be added to the search.php theme file (probably). But the exact location and details vary from theme to theme, so you might have to ask the theme author for guidance as well.