You can use Bitmap.GetPixel. It's slow, but it may be fast enough for
your purposes. You wouldn't want to use it if you needed to look at each
and every pixel, but in this case that shouldn't be necessary.
The fast way to work with Bitmap data is to use LockBits, which returns an
IntPtr. I'm not sure whether you need unsafe code to manipulate that or
not, since I haven't done that sort of thing in .NET yet.
I'm not sure what the second clause in the sentence has with the first.
That said...
"Divide and conquer" always implies multiple passes (or at least the
potential for multiple passes...when you're lucky, the algorithm requires
only a single pass

).
In this case, Ben is suggesting (I believe) that you "divide and conquer"
relative to finding the top and bottom of the rectangle. If the rectangle
you're looking for does not straddle the vertical line in the middle of
the containing rectangle, then you conceptually split the containing
rectangle into two halves on that vertical line, and run the search again.
Keep doing this until you find a vertical line that _does_ intersect the
rectangle you're looking for.
When you do find a vertical line that intersects the rectangle, then you
necessarily also have found the top and bottom Y coordinates of the
rectangle. Using those coordinates, select a horizontal line to scan (it
could be any line between the top and bottom, and Ben suggests simply
using the average of the top and bottom Y coordinates), which will in a
single pass across the containing rectangle tell you the left and right X
coordinates of the rectangle.
Note that the "divide and conquer" part of the algorithm should be done as
a breadth-first search. That is, rather than completely searching one
half, and then completely searching the other half, do the initial search
of the middle of each half first, and only if that fails to find the
rectangle would you do the "divide" part of the algorithm. The reason
being that if you do it depth-first, you have a 50/50 chance of having to
visit literally every pixel in the half that _doesn't_ contain the
rectangle, which is obviously counter to the whole point of doing the
search quickly. You might as well just start doing the vertical scans at
the left and work your way right.
I sure hope this isn't a homework assignment. I hate doing people's
homework for them.