First off don't panic, The Atahualpa options are stored in teh WordPress database.
To make sure I understand, in the WordPress dashboard under APPEARANCES you should see:
Add New Theme
Atahualpa Theme Options
Are you saying the APPEARANCES section is gone? If so, then Yes I think something they did may has caused this problem and they may have messed up the WordPress code itself.
1) backup your database - If you don't know how to use phpMyAdmin you can use the plugin db-manager
2) since the last thing done was the contact form-7 use an FTP program to access the site and go to wp-contents/plugins and first copy the contact form 7 folder to your local machine, then delete it from the server. This will remove it and now try th ebackend again
if that doesn't fix it, then you may need to overlay a new copy of the wordpress code, but take it one step at a time so....GO BACKUP YOUR DATABASE RIGHT NOW.