Is it possible to hack an airplane while it's moving (in general)?
The answer to 


  Is it possible to hack an airplane while it's moving?


is "theoretically yes, movement has no effect on a plane hackability".


  How can someone "touch" a moving airplane, have the time to identify it and then to hack it?


All the people inside the airplane are touching it during the whole flight, they know which airplane they are flying with, and they have a flight worth of time.


  How can someone, without having specialized machines, can hack an airplane?


Theoretically, for some components, you don't need specialized machines (see below), you need a laptop and an ethernet cable

see here (TL;DR version ), or here, and finally, from here


  First, the airplanes. The problem the GAO identifies is one computer security experts have talked about for years. Newer planes such as the Boeing 787 Dreamliner and the Airbus A350 and A380 have a single network that is used both by pilots to fly the plane and passengers for their Wi-Fi connections. The risk is that a hacker sitting in the back of the plane, or even one on the ground, could use the Wi-Fi connection to hack into the avionics and then remotely fly the plane.
  
  The report doesn't explain how someone could do this, and there are currently no known vulnerabilities that a hacker could exploit. But all systems are vulnerable--we simply don't have the engineering expertise to design and build perfectly secure computers and networks--so of course we believe this kind of attack is theoretically possible.


As we read here, though, safety critical components are not that easy to compromise:


  it’s essential to understand that aircraft systems can’t be updated in-flight or on the fly. This means that if an attacker is seated on the airplane, there’s no way they could modify systems. There are only three ways to update a system on a modern aircraft:
  1. Take the hardware off the aircraft and return it to the manufacturer for a factory performed update.
  2. Some larger airlines have their own maintenance organizations with the required specialized equipment to perform a bench update of a particular system using a portable data loader (PDL) or some other type of specialized data-loader.
  3. On-wing update [...] Specialized hardware (physical switch(es)) must be set, to place the IMA and relevant systems in maintenance mode. Once the aircraft systems are in maintenance mode, a maintenance engineer needs to follow a sequence of steps to push the update to the target system. The concept of an automatic update does not exist for any safety-critical system.


So, to summarize: yes, researchers have identified non-critical systems that could be hacked (as the passenger entertainment devices), but so far nobody has demonstrated the feasibility of hacking a critical system