Does this diagram illustrate the second law of thermodynamics? why or why not

The diagram is not showing the second law of thermodynamics. It is the demonstration of 1st law of thermodynamics.

Second law of thermodynamics describes the entropy of the system increase with time, it does not decrease with time. It is constant for ideal systems.

While in first law of thermodynamics, it is stated that the energy of a system can not be lost but it is transferred from one form to other form.

And in this picture, it is shown that the energy released from heat source to cold sink is used in doing work.

Work and heat are forms of energy.

No, it does not because the diagram shows all the thermal energy added to the system being transformed into work. The second law of thermodynamics states that engines or machines cannot be 100 percent efficient because some thermal energy is released to the surroundings.

beta is electron from nucleus

something from nucleus has changed, but charge must be same for cons of charge