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I don't know exactly what it means when there is something like a penalty factor in a specific material property. What criteria should this value be entered with?

Additionally, I am not sure what the penalty method of constructions means in the analysis process and how appropriate the alpha value is. Is it similar to assuming that there is something like a strong spring?

In general, Penalty is a way to enforce approximately a constraint.

The rule is:
You need to find a penalty number that is large enough to impose the constraint, but not too large, otherwise the system matrix will be ill-conditioned.

The typical rule for the Constraint handler (at the analysis level) is to:
1) evaluate the typical stiffness of your model (for example, in frame elements, you can take K = EA/L)
2) compute its order of magnitude: oom = round(log10(K))
3) compute the penalty value alphaS and alphaM as 10^(oom+8).
Why "+8"? Because a floating-point number (in computers) has 16 significant digits, so adding 8=16/2, to the larger order of magnitude, will be halfway between the accuracy of the constraint, and the numerical conditioning of the stiffness matrix.