How to check if the results accurate upon activating stabilization in step? 1

Check viscous forces (VF), they should be sigificantly smaller than overall forces. Also compare viscous damping energy (ALLSD) and total strain energy (ALLIE). This ratio should be smaller than the dissipated energy fraction (default value is 2*10^-4). There's a chapter "Ensuring that an accurate solution is obtained with automatic stabilization" in the documentation. I recommend reading it along with the whole "Solving nonlinear problems" part of Abaaqus Analysis Manual.

overall forces you mean like which one?
I see some people talk this way:
Now just sum up ALL SD+ALLCD+ALLVD and divide it by ALLIE and establish the dissipation percentage.
Practically, damping dissipation shouldn't be more than 2% as it would affect the physical system. Choose the damping for which 1.Solution converges and 2.The dissipation % is a minimum
How do you say about that?
An should I also compare kinetic energy with something?

In case of the use of stabilization I was taught to compare ALLSD vs ALLIE or ALLWK. When it comes to viscous forces you just have to make sure that their order of magnitude is far enough from global load. So for example choose the load application point and plot load vs displacement and then viscous force vs displacement and compare these plots as explained above. If you check both these energies and VF it should be enough to make sure the results are correct.

I definitely agree that this artificial damping should be as low as possible so that it won’t affect the solution too much. On the other hand it must be enough to enable convergence. However remember that you should always make sure that there are no errors in your simulation causing non-convergence as automatic stabilization may help complete the job but results would be incorrect anyway in this case.

When I don't activate stibilization in step, It does not converge. however, when I use stibilization with different values ranging from 2e-4 to 2e-10, I get convergence and all the results are exactly the same (load-displacement). Is it possible?
Thanks

Sure, stabilization is meant to be used in cases when it's hard for the solver to achieve convergence (especially analyses with contact where rigid body motions occur before it initializes or highly nonlinear cases such as buckling or crack growth). It's also designed in such way to have very little to no impact on the results. That's why usually it is advised to use low values, close to default one.