Hi!
Not sure, those does not seem to be related to the search. I have checked the code part, but it is not shared within the two plugins. These should not cause a white screen either, as those are only warning messages, not fatal error reports.
Anyways, I have quick-fixed these issues on a test server. Can you please try replacing one of the files:
1. Open up the wp-content/plugins/related-posts-pro/includes/related_content.class.php file on your server
2. Replace it’s content with this
3. Save the file
The error reports should go away.