Linguistically, the difference between "he died" and "he's dead" is called aspect. As for your specific sentences:
"I thought he died" -> There was some event that ocurred which I witnessed or which I was made aware of in someway which I thought had resulted in him dieing.
"I thought he was dead" -> My understanding was that for some time up to now he was a corpse (or in some other such state). I do not necessarily know about the time or event in which he died.
Have you read the authors current series, Dai Dark? I've only read a couple of chapters so I can't say too much about how it compares to Dorohedoro, but...