Based on example sentences in several online dictionaries, I have the impression that "ballpark" is used in situations where you really don't know and can't know the exact number but want to make an educated guess. I'm not sure if it's accurate to use "ballpark" for a guess about a number we forget.
As you say, a "ballpark" number is an educated guess about a number that we never knew, a number that is "somewhere in the ballpark." (It's an American idiom, since a "ballpark" is a place where people play baseball.) To convey your meaning, you could say one of these:
I can't remember the exact number, but a ballpark number is 250.
I can't remember the exact number, but 250 is somewhere in the ballpark.
You would not convey, by referring to a number as a ballpark number, that it was a number that you knew and had forgotten. You would have to state that.
Correct. Example - The world's population is in the ballpark of 8 billion.