Hi Michael,
Thank you very much for your feedback, let me know if anything changes.
3. In that case, maybe placing the plugin into a container that has a max width, or adding a max-width custom CSS property to avoid too wide search sizes might actually do the trick. Let me know if you need help with that.
Q1
There is a search results cache as well, but that is disabled by default: https://i.imgur.com/LLlQFtU.png
I only recommend enabling this options if there is a very highy expected number of searches, the database actually does have a built-in cache mechanism, that performs in regular cases just as good. If this option is enabled, the cache is stored in the wp-content/uploads/asp_upload directory. It also contains the dynamically generated CSS files.
Q2
That is correct. It works exactly as you described.