Database Upgrade Required and site down

Help! 2 of my WordPress sites are down and both are experiencing different problems. Both hosted on Dreamhost.

https://www.smallhousestyle.com
The site isn’t loading properly:

Fatal error: Call to undefined function gajaxsearch() in /home/.manchu/smallhouse1/SMALLHOUSESTYLE.COM/wp-content/themes/grid_focus_public/searchform.php on line 2

Here is line 2:
<?php gajaxsearch(); ?>

If I clear line 2 then the site generates another error:
Fatal error: Call to undefined function adsensem_ad() in /home/.manchu/smallhouse1/SMALLHOUSESTYLE.COM/wp-content/themes/grid_focus_public/third.php on line 16

If I clear line 16 the home page loads correctly but then the posts have issues…

What is going on?

When I attempt to login to the admin I get the following notice:

Database Upgrade Required
Your WordPress database is out-of-date, and must be upgraded before you can continue.
The upgrade process may take a while, so please be patient.
Upgrade WordPress ?

Then the following error:

WordPress database error: [Unknown column ‘user_nickname’ in ‘field list’]
SELECT ID, user_nickname, user_nicename FROM wp_users
Fatal error: Cannot access empty property in /home/.manchu/smallhouse1/SMALLHOUSESTYLE.COM/wp-admin/upgrade-functions.php on line 653

Here is line 653:
$all_options->{$option->option_name} = stripslashes($option->option_value);

Does anyone out there have a clue as to why this would happen and what I can do to fix it?

Also…
https://www.parkguitars.com
is not loading properly. Only the header is loading but I am not getting any of the errors as above.

Thanks for your help.

Best,

Jared