What does an external observer see if you shine a laser pointer while crossing an event horizon? If I understand correctly, the event horizon of a black hole is the boundary beyond which we cannot perceive or describe any events, and all objects appear to freeze when falling in until their light is redshifted out of visibility. How would shining a laser pointer (pointed at the observers spacesuit or something where they’d be able to see it) affect what the observer saw at the point that you crossed the horizon? Would the dot on their suit disappear when you crossed the horizon, and wouldn’t that count as an event they were able to describe? 
 A: You are not saying it, but I will assume that the laser creates visible wavelength photons. As the falling in laser pointer closes up to the horizon, the photons coming from the pointer are getting redshifted on your (the far away observer) suit, until they are not in the visible range any more. At this point the dot disappears. 
Though, the dot is still there, just not visible (the photons are not in the visible range) anymore. Photons are still coming from the pointer onto your suit in infrared, micro or radio wavelength.
You are not saying it, but if you put a receiver photon detector on your suit, you will detect these photons still coming until infinite time theoretically.

But where things get odd is we calculate the time taken to reach the event horizon in our co-ordinate system as observers sitting outside the black hole. This is an easy calculation, that you'll find in any introductory book on GR, and the answer is that it takes an infinite time to reach the event horizon.

How can anything ever fall into a black hole as seen from an outside observer?
Though, when the photons fall below the Hawking radiation of the BH, it will not be possible to detect them anymore.

In fact see A.V.S.'s comment below: the photons pretty rapidly drop below the background Hawking radiation from the BH in fact, so it really is the case that the infalling object becomes undetectable, even in theory.

Time of flashlight crossing the event horizon as seen from an external observer
