I think means:
"He was looking at some distinct location in the distance."
I think both mean:
"He was looking off into the distance and looking for anything unusual."
So, what is the grammar of #3?
Doesn't "を" require an object?
Has "遠く" been nominalized somehow?
I heard #3 in an 男っぽい dialogue.
Maybe the words that are needed to create proper grammar are not spoken?