perplexing question

For some reason, I feel like the answer to this question is just out of my reach. Like when something's on the tip of your tongue and you just can't think of it.  So here goes.

We know that Newton's First Law of Motion states: In the absence of force, a body either is at rest or moves in a straight line with constant speed (basically, once you start moving, you'll keep moving unless something changes). We know that a point on the outside of a rotating disc is necessarily traveling faster than a point closer to the center of the same rotating disc in order to cover a greater circumference in the same amount of time. We also know that gravitational force exerted by an object increases as distance between objects decreases according to the equation: PE = -G*(m1*m2)/r; (where G = gravitational constant, 6.67*10^-11; m1 = mass of object 1; m2 = mass of object 2; and r = distance between center of object 1 and object 2). And we know that light does not escape black holes and can even be bent by the extraordinary gravitational pull from a black hole.

So here’s the question: If light (we’ll name him Jim) were to approach off-center of a black hole (we’ll name him Bill) but within the very edge of the event horizon (the point at which nothing can escape Bill), Jim would supposedly spiral towards Bill’s center (remember that Bill is three dimensional and equally strong in all directions, much like myself after 5 days of camping). In order to continue moving inward (hence the spiral) Jim would have to have a continuous force acting radially from Bill’s center (Newton’s 1st Law), which force is actually increasing according to the boring equation referenced in the previous paragraph. So if the force is increasing as Jim get’s closer to Bill, the distance between the annuli of the spiral (as measured radially) must be increasing. So far, this means that if you were to draw a line (we’ll call her Cathy) straight out from Bill’s center and if Jim were to make one complete revolution at the beginning of his journey in some given amount of time, he will make one complete revolution towards the end of his journey (after spiraling inwards) in much less time because he has a much shorter distance to travel (if it were a circle, the circumference would be much smaller), and the distance between annuli as measured on Cathy is also increasing.

Okay, we haven’t gotten to the question yet. But we’re getting more confused.

Anyway, the spiral traced by Jim as described would probably approximate a Fermat spiral or at least the first half of a Fermat spiral. So if you were to be a casual observer (we’ll call you Otis) and could watch all of this happen (which you couldn’t really) from a fixed point in space outside Bill's event horizon, would it appear as though Jim sped up, slowed down, or didn't change speed has he approached Bill? Also, if Jim were aimed directly at Bill, would he speed up as he approached Bill and was acted upon with ever-increasing force by Bill’s overwhelming gravitational pull even though the speed of light is supposedly as fast as anything can go? Also, also, who names their kid Otis?