I am watching this video about lumped matter discipline, and I'm not sure for what is it used? Why and how we can make dq/dt be zero? What LMD says about circuit element? Does dq/dt represents excess of charges because of non ideal element?
This is all about assumptions simplifications and reduction of complexity. Of course, there's never such a thing as a lumped element in reality. Because charge is quantized and thus you can't achieve dq/dt=0.
But you can set your boundary conditions and parameters for your circuit in a way that an imaginary lumped element is so close in its behaviour to a real element, that the error will be neglegible.
You ask about benefits? Lumped elements make analytical calculations about circuits with use of pen and paper possible in the first place. Yes, nodal analysis and use of KVL and KCL are unthinkable without defining your circuit elements as lumped ones in advance!
LMD says about elements, that if you draw an element with two terminals in your schematic, you assume, there is no third terminal!
Example for dq/dt problem: given you have a circuit consisting of a big battery and a parallel plate capacitor. Hence it has two nodes. After connecting the circuit, a current flows for a short time. The assumption, that the capacitor is lumped means that the same amount of charge that leaves the capacitor through one terminal enters the capacitor through the other one at the same time.
Now let's connect one of the nodes to earth, which changes nothing. But then you go to the capacitor and put your finger in vincinity to the not grounded plate. Due to influence some charge flows through your body and accumulates in your finger and the opposite in the plate near your finger.
As you can imagine dq/dt is no longer true for the capacitor. Charge enters at one terminal which does not leave at the other. If you draw this capacitor in a classic way in your schematic and try to do nodal analyis, you fail. LMD is violated here.
Now we can see, LMD has two sides. It is an assumption about circuit elements which allows us to draw schematics to describe the behaviour of ciruits. But on the other hand we have to make sure, that the assumption is very close to the facts.
In general you have some indicators whether a circuit can be described by lumped elements or not. If the minimum wavelength is greater by an order of magnitude than the dimension of the circuits you are fine with LMD.
If not, you can have a look at the elements themselves. And furthermore you can introduce more lumped elements to describe the behaviour of the mismatches.
In our example with the parallel plate capacitor we can add an extra capacitor describing the capacitance between your finger and the plate of the cap, which again is a lumped element.
In RF you often encounter schematics depicting a simple wire as a concatenation of Ls and Cs. This breakdown is used to bring the behaviour of transmission lines into lumped elements. These lumped elements are just a representation of the behaviour of a transmission line but — again — allow a classic nodal analysis.
So LMD is a tool for abstraction. By declaring elements as lumped you can simplify calculations by several orders of magnitude. But you have to make sure, that all assumptions produce only tolerable errors in comparison with the real circuitry.