How easy is it to make a connection to the aircraft pitot-static system? I've recently discovered the device named Levil 2 AW which gives complete navigation functionalities, including Air Data computations once it is connected to the pitot-static system.

In this regard, generally speaking, is it really so easy to connect to the aircraft pitot-static system as it appears from both product description and related videos?
It's very easy to connect a component to the pitot and static systems: It's literally just basic plumbing (install a T fitting and connect the lines). For IFR certified aircraft a static system test will also be required (and a pitot pressure leakdown test would be advisable if the pitot system is opened).

The regulatory issues surrounding the installation are more complex regarding what kinds of devices may be installed on a certificated airframe and under what conditions they such devices could be used as a primary or standby reference for flying the aircraft, as Ron alluded to.