When a plugin is deactivated, there is no way for it to affect the page output, as the code is not running, not included whatsoever – it is as if it never existed on your site. If the issue persists even if the plugin is not enabled, there is no way for it to cause the problem.
The issue still appears even by adding any random shortcode to the shortcode box, you will see the error with the search deactivated: https://i.imgur.com/rMgcsvo.png
It has something to do with the shortcodes widget output, but I am guessing this is triggered somewhere else, probably in a plugin. Deactivating then one by one and checking the ouptut should lead you to the one causing the problem.
For the second issue, can you please check the FTP access? I will check and try to debug the code. With the current access I was able to connect, but I can not list the directories. Thank you!