Does a trend line always pass through every point on a scatter plot?

No, it does not and it's not supposed to.  A trend line is drawn to go through in the best way possible, to go through the "center" of the points as best as it can.  It may hit some of the points, but not all of them.  Generally, the idea is to try to get the trend line to have as many points "above" it as it does "below" it to say you've gone through them evenly.