It's fictional, the overall design of the cable towers is taken from Arecibo's, FAST's towers are distinctly different. It's clearly neither though as the surrounding topology is flat and mostly devoid of trees, both FAST and Arecibo are nestled in valleys dense in foliage. That sort of layout doesn't play well in video games.
I don't think it is, since FAST (finished 2016) wasn't finished until well after the game had been released (2013)—on the other hand, parts of it were built (FAST was started 2011), so perhaps there was partial inspiration? I'm honestly not sure, but certainly a lot of the design is much more similar to Arecibo (if memory serves me right).
I also haven't played the game in years, so take this with a grain of salt :)
I mean, yes, obviously it's not literally the Arecibo telescope in the same location, but it's a heavy inspiration and quite similar in design and structure. (For example, an obvious difference in BF4 is the surrounding forest, which not as dense as in Puerto Rico's location.)
I would say it takes inspiration from Arecibo over FAST but it's clearly neither. The surrounding topology is flat in comparison to either and there isn't much of a forest to speak of. It's clearly a level design that takes inspiration from reality.
