Hi,
1. & 4. Please note, that 3rd party customizations are not part of plugin support. The layout of the results page is fully controlled by the theme you are using, unfortunately there is no way for a plugin to change that (except using a custom page builder of some sorts, but many themes do not support that).
This all has to be custom coded I’m afraid, and custom CSS will not help, it is much more complicated than that.
I have looked at the template, and managed to add the search form to the search results page, that was quite simple. Please make sure to have a copy of the search.php file in your theme directory, which contains this change. Any theme update may override that, and the changes will be lost.
To display images, change the pagination, custom layouts etc.. are way beyond this support – I suggest asking a developer to make those changes to the theme via a child theme file. It should not be too difficult, and the plugin has a set of theme related functions a developer can use to get information from the search objects.
I am more than happy to assist if there are any technical questions about the usage of the plugin API or anything simlar.