Should I Plot my Learning Curve Depending on Various Parameters to Diagnose Overfitting/Underfitting or is One Parameter Sufficient?
Overfitting is a result of the entire model. It is best to visualize every part of the model to understand how the combination of elements is overfitting.

Ideally, you should visualize all elements on the same interactive figure so how the combination is overfitting. If that is not possible or the interpretation is difficult, then many single element visualizations would be an option. However, that increases the possibility of missing interactions causing overfitting.