Your Relevanssi settings are indexing the post author name, but I suspect you mean the taxonomy imho_author, is that what you want included in the search.
You are not indexing that taxonomy, and hence it is not included in the search.
I can confirm on the front-end that searching for the author doesn't work.
I went to the Relevanssi settings to confirm them and re-built the index.
I noticed the warning shown in the screenshot. Relevanssi itself is warning that it might not work correctly because your server is missing the common mbstring PHP module.
I suggest you contact your host and have it activated, it is a common module that is also required for Toolset.
I suspect that you will find PHP notices in your debug logs because of this.
I couldn't see why the Toolset settings page was blank. I temporarily de-activated the plugins you use to customise the admin pages but that didn't help.
I suggest you first look in debug.log to see if there are any related messages.
If you haven't already, turn on the debug log by editing your wp-config.php file and change the line with WP_DEBUG like so:
That will create a debug.log file in your wp-content directory which you can examine in any text editor. Try visiting Toolset > Settings and then inspect the log.