1) How do you get better at this? Is it just memorizing pro games or does it just come with time? 2) Does it actually improve your game or is it just sort of nice to have. 3) At what point should I actively try to improve on this?
In my experience, memorizing games is more of an effect than a cause: Memorizing games won't improve your own game so much as improving your own game will help you memorize them.
Fundamentally, Go is all about recognizing and applying patterns, and the more patterns you have in your arsenal, the easier it is to recognize and apply them in the future (be that during actual gameplay or memorizing). The trick when memorizing pro games is seeing those patterns and understanding exactly why a pro made a particular move; when the intended result is understood, the progression of stones toward that result tends to flow naturally. Well, as naturally as they can considering the opponent is usually going out of his way to stop it.
(Side note: Attempting to memorize low-level amateur games is often an exercise in frustration and futility because so many of their moves don't (seem to) make any sort of sense at all.)
As far as actively trying to improve your memorization, I'd say focus on your own games; if you can't yet replay your games more-or-less from scratch, learn how. Not only is the ability to recreate and review troublesome situations after a game you just played an invaluable learning tool, but this is typically far easier than memorizing pro games: Unlike pros who tend to be thinking a thousand moves or so ahead, you (presumably) know what you were actually thinking when you made each and every one of your moves.
Of course, if you weren't thinking when you made most of your moves, you might want to work on that first.
Memorizing pro games can be nice, but I'd use that more as an exercise in how well you actually understand them than an end in and of itself. You don't want to just be all "And then white played at j10 and then black played at j11 and then white played at o9 for some reason" so much as "White extended, black blocked and then white threatened black's weakness on the right side to give himself some more room to maneuver". The first is only useful if the board position in your actual game is more-or-less exactly the same (which, let's be honest, will never be the case), while the second can be abstracted out and applied to almost any scenario.
Try to reproduce a game that you have played immediately after the game finished. You can do it collaboratively with your partner. It helps to get through the thoughts behind the moves again and to analyse what went wrong.
I don't think it is necessary (nor really useful) to have a long-term memory of Go games learned by heart. Instead, you need learn good moves, good shapes and crucial points, i.e., abstractions of concrete games.