Do aircraft really have text communication over FMC? I saw a photography that is obviously Photoshopped that sparked my curiosity 

Does aircraft have text messages transmission? Can text messages or text strings be transported over the air like transmitting METAR strings over a frequency like ATIS? I remember something about in flight printers that would print hard copies of mid-flight flight plan changes so perhaps something like that can be theoritically used for transmission.

In a simple manner. Is communication over FMC ever done?
Yes. Text messaging over ACARS has been commonplace since the 1980s. It is air-to-ground and ground-to-air, not air-to-air. It is commonly used to exchange flight plans, weight and balance data, ATC clearances, schedule updates for passengers' connecting flights, and other operational purposes, but also sometimes for fun (e.g
birthday wishes, sports game results). It's primarily used between an aircraft and the airline's dispatching department, but can also be used directly between the pilots and ATC under some circumstances.