He must have been trying to pull a fast one on you to see if you were all asleep. There’s no way you can take the Newtonian gravity equation (F=m1m2G/r^2) and have the speed of light fall out of it. If one of the masses is infinite, there will be an infinite escape velocity (according to my bar-napkin calculations, escape velocity is V=SQRT(2m2G/d) ).
So this equation has nothing to do with the speed of light, unless he threw in some relativistic equation into the mix, and if he did this, he manages to come up with the wrong answer.
That’s a bit of an oversimplification, which may be part of your confusion-- You’re right, though, that photons lose energy by redshifting. A better statement of what goes on at the event horizon of a black hole, is that every possible path ends up getting you closer to the singularity.
You can do that, but that’s not what escape velocity is about. Consider an empty space with just the Earth floating around. If you throw a ball slowly, it will come back down to earth. The faster you throw, the farther it gets before earth’s gravity slows its upward velocity to zero and it starts falling back down. But if you throw it really fast, the ball will travel away from the earth forever - it can go infinitely far away and still have an ‘upward’ velocity. The minimum speed you need for this is the escape speed.