And Is Option (D) incorrect because
1. Parallel elements contain a "breaking" (a participle) & work (a verb)
Yep. "Breaking" is not a verb. "Work" is a verb.
(I don't know/remember the term "participle", so I can't say for 100% sure whether you're right about the terminology "” but that's immaterial; the distinction of verb vs. modifier is the key.)
The way choice D is written, the only thing that's allowed to be parallel to "more than half the residenst work..." is "twelve hospitals were investigated..."
Those clearly aren't intended to be parallel structures, so that choice makes no sense. (As you've already pointed out, the grammar disallows any sensible interpretation.)