Sorry to hear about the problem you are having.
Could you please tell me which version of PHP and WordPress you are using on your website?
You can resolve your PHP timeout error as described below.
https://wpastra.com/docs/increase-php-time-limit-wordpress-sites/
How To Change PHP Time Limit WordPress?
How to Increase PHP Time Limit for a WordPress Site?
This can be due to plugin conflict on your site so please try temporarily deactivating all plugins except the Ivory Search plugin and see whether everything works fine, and then enable the plugins one by one to see which plugin is conflicting if any.
Best regards,
Ivory Search Support