CiviDiscount db update error
I can only speak in generalities, as I use Drupal instead of WordPress. So some of these things might be in a different spot. You'll need to go to wherever WordPress has its permissions and set them there. It's possible that they have it set up so that all the permissions go through the main site or that they are individual to each site. 

Here's where I turn on error handling on my install. 



Some options will tell you they are not recommended on a live site. That is because they slow down your site and may show errors to the general public. Usually if I am having issues, I will turn them on temporarily so that I can get the errors to show and then turn it off once I am done.

The extension not being found is likely due to one of two things:


The site is pointing to the wrong place for extensions.
Permissions for the files. I get this when I am logged in as root to the server, but the files need to be "owned" by the user assigned to the account.