Translation:And then I found this letter in the post office box.
No, a "Postfach" (post office box) is at a post office and a mailbox is in front of someone's house/home.
"im" = "in dem", so whenever you need a definite article with neuter or masculine nouns
I used "past office box" in one exercise. That was accepted, but it gave "lock box" as an alternative. Then it told me that "lock box" is wrong here. I've reported that one of these is wrong.
That is not really correct English imho. You should say "And then I found..."
The "I did find" construction could be used but in a different context, e.g. when you want to emphasize that you did find something (as opposed to not finding it) e.g. "I thought I'll never find it, but in the end I did find it!"