This is what I have received from the theme author:
1) Invalid HTML would not cause the whole page to go blank, besides the search results work in some cases. This is very unlikely to be the issue.
2) The theme uses the jQuery version that comes with WordPress, as any theme should. All up-to-date plugins should work with this version.
3) Your error console does not show any JS conflicts.
4) The theme has already been run through Theme Check prior to be sold on ThemeForest.
With the thousands of plugins out there it's simply not possible to make the theme work with all of them unfortunately. My last suggest is to enable WP_DEBUG in your wp-config.php to see if it returns an error when the search query is run.
At this point maybe it is a good idea to talk to your developer and see about hiring.
If you could put him in contact with me that would be appreciated.
Thanks for your time.