The simple past expresses the past action or event as something that occurred in the past. The present perfect expresses the past action or event as something that occurred in the past, but from a point of view that recognizes its implications for the present.
With What has he done? the speaker casts his deed in the light of its implications for the present. The deed is not over and done with. (There will be ongoing consequences. He will have a trial, the newspaper will run stories, and so forth.)
With What did he do? the speaker is expressing interest in the particulars of the deed without reference to their ongoing implications.
What happened to him? wants to know what befell him, an accident or an acute medical condition, etc.
What has happened to him? wants to know what put him in the hospital and whose effects he continues to suffer from. If we learn that someone has died in the hospital, we would not be likely to ask "What has happened to him?"