I would say only #1. "Opening the drawer, he took out some papers."is correct. In the construction for the other three, the clause following the participle isn't connected causally or temporally.
For example, in flipping through the pages of the magazine, I saw a photo of an old friend.
You were able to see the photo because you were flipping through the pages, and also you saw the photo while you were flipping through the pages.
Having become a seaman, he did xyz . feels much more comfy.