Hi!
Thank you very much for your kind words!
I see you are using the compact box layout in the header. You can set the final width of the search bar here. By default it uses 100%, which is the same width as the container element (where the plugin is placed). Use a pixel value, like 320px or so, to give an exact with for the search bar.
To display the same results on the results page as the ones in the live results list, please make sure to enable the search override feature. If it has no effect, then try this as well.
If still no luck, then check if you have any other search plugins active, and make sure to turn them off- as well as any other plugin, which may override, change or do anything with the results page.