Hi!
1. By “to keep the search results location to be disabled” do you mean like to keep the results position fixed in one position and not be able to scroll away from it (even when reaching results bottom)? I’m not sure if this is possible, as the scrolling event automatically propagates back to the browser.
2. It’s possible by adding an additional script to the site footer. Put this to the footer.php file in your theme directory, right before the closing body tag: