This question might appear as an evidence, but I'm just a noob in that topic.
I'm following the JST since launch and see that its speed is considerably decreasing : Is that due to gravity of the system sun, earth, moon?
Correct. As the craft goes away from the Earth and Sun it is slowing down. Like throwing a ball up, it’ll slow down until gravity pulls it back down, but, JWST is beyond escape velocity, it’ll slow down, but, not enough to fall back to Earth. If they do nothing else, it’ll go into a solar orbit, but they will slow it at the right time to stop it at the L2 position and keep it there.