Googler, Christine, has confirmed a bug where the Google Custom Search Engine stopped working properly on the popular CMS package, Drupal. The bug has been confirmed to be resolved in a Google Custom Search Help discussion forum thread.
Thanks for the heads up about the issues with Drupal sites and CSEs, and for all the details you provided about this. Your CSEs should now be showing results rather than your search engine homepage in your page's iframe.
We've reverted the change that caused the incompatibility with the "query" parameter, and we'll try to ensure that these parameters don't cause problems in the future.
I am personally a fan of the Google CSE, I use it on this blog, my personal blog and many of my web sites. There are limitations, i.e. not real-time results - but on many blogs, the results are close to real-time.
Drupal is a very popular CMS, so I am glad this bug is now resolved.
Forum discussion at Google Custom Search Help.