Unfortunately, PHP's fatal errors are not particularly debuggable because they don't give a backtrace. Both of those errors are in functions that are related to MySQL (the former fetching data, the latter closing a statement).
It's certainly possible that there is an add-on involved that seems to be tripping for this particular user. It's very hard to say.
That said, I will note that you have your maximum search results set to quite a large number. I ran a search for a user's content and it gave over 1900 results, so I'm assuming the max is 2000. This is 10 times the default. When a search is run, the permissions are checked for every matching piece of content. This setting has a direct influence on the amount of data retrieved from the DB and the amount of work done to verify the permissions.