...since there was never any actual evidence of his death?
I know there are recently leaked documents pointing to the possibility but I assume back in 1945 those were classified so the general population never knew about them.
But did people (of any country) in the mid to late 40s and 50s ever question this possibility, or just believe that he was definitely dead because the Russians said so?
Furthermore, since those now leaked documents do point to the possibility Hitler survived, did any government agency ever attempt any serious investigation to debunk them?
There was substantial concern. In fact, when General Eisenhower first returned from Europe he held a press conference in which he expressed the belief that Hitler may have been alive. His words:
Press: Do you think Hitler is dead? Are you convinced Hitler is dead?
General Eisenhower: Well to tell you the truth, I wasn't. I was at first. I thought the evidence was quite clear. But when I actually got to talk to my Russian friends they weren't convinced, and I found that it had been erroneously reported from Berlin. I don't know. The only thing I am sure of is what I said in my conference -- if he is not dead he must be leading a terrible life for a man that was the arrogant dictator of 250,000,000 people to be hunted like a criminal afraid of the next touch on his shoulder. He must be suffering agonies of the damned if he is alive.
The transcript: http://www.eisenhower.archives.gov/research/online_documents/holocaust/Press_Conference_1945_06_18.pdf
That being said, the conclusive consensus is that Adolf Hitler died of a self-inflicted gun shot as is commonly known. There is the eye-witness testimony of two SS orderlies, as well as dental records matched with a piece of burnt jaw recovered from the site to corroborate the story.