When I flush, the deposit goes down, then water comes up and continues to run as if the water just circulates forever... well, until I open the led and shake the black container.

The fill valve,it has rubber gaskets inside it that,with time,go bad, being that they are constantly exposed to some kind of moisture.

Any handyman or plumber can replace this valve,it takes less than 1/2 hour.

Sounds like you have a bad flapper valve, Feel around the flapper flat edge. If it's wavy or you feel rough spots replace the flapper see the image,
The linkage between the flapper and the flush lever should have 1/4" play when the tank is filled. Also, check the small tube coming out of the top of the ballcock and make sure it's connected to the white overflow tube and draining water in to the tube.