It took me an hour to place my whole head within the opening so far that I could see him as he lay upon his bed. (3)
This strange time management technique suggests extreme loneliness. We learn later that the narrator has problems sleeping at night (and probably during the day). This moment is when we first begin to notice there's something funny going on with time.
And this I did for seven long nights – every night just at midnight. (3)
It seems Poe is reminding us that we are in fact in a Gothic tale, where all bad things have to wait until just after midnight before they can play.
A watch's minute hand moves more quickly than did mine. (4)
This is an amazing line. The narrator sees himself as a kind of clock, counting down to the old man's death.