Can I edit theme CSS without FTP access to the files? Can I edit Drupal theme CSS files with out the ability to download/upload css files using FTP?
Without server access of some description either via FTP or SSH (for example) - you can't edit the files.

You could, however, try CSS Injector if you are able to install modules through the UI.


  Allows administrators to inject CSS into the page output based on
  configurable rules. It's useful for adding simple CSS tweaks without
  modifying a site's official theme -- for example, a 'nighttime' color
  scheme could be added during certain hours. The CSS is added using
  Drupal's standard drupal_add_css() function and respects page caching,
  etc.