Hi,
Unfortunately the auto-poulate only works on the page load, it is not possible on the search input click, that would have to be custom coded.
The index table engine may help you with that, it should make a great performance impact, especially if you are having a lot of posts.
The results page layout is unfortunately controlled by the theme you are using, the plugin cannot affect that.
and how to set breakpoints for mobile and tablets, not the post size breakpoints but the actual plugin breakpoints for results
What exactly do you mean by that? Styling (width, height etc..) of the search bar, or live results list, or the results page?