Oh, wow, you should update. We’ve made a lot of of big advancements since the original version. The issue you’re asking about with the search form URL has been fixed, as well. I remember that one specifically a few months ago for when people are setting up their site URL in a different location than where they actually have WordPress.
http://themeblvd.com/changelog?theme=akita
And sure, if you want to copy searchform.php to your Child theme, you can.