Mean centering before PCA
PCA is more or less per definition a SVD with centering of the data.
Depending on the implementation (if you use a PCA from a library) the centering is applied automatically e.g. sklearn - because as said it has to be centered by definition.
So for sklearn you do not need this preprocessing step and in general you apply it over your whole data.
PCA is unsupervised can be used to find a representation that is more meaningful and representative for you classes afterwards. So you need all your samples in the same feature space via the same PCA.

In short: You do the PCA once and over your whole (training) data and must be center over your whole (traning) data. Libraries like sklarn do the centering automatically.
I am unsure if this kind of question (related to PCA) is acceptable here or not.
However, it is suggested to do MEAN CENTER before PCA, as known. In fact, I have 2 different classes (Each different class has different participants.). My aim is to distinguish and classify those 2 classes. Still, I am not sure about MEAN CENTER that should be applied to the whole data set, or to each class.
Is it better to make it separately? (if it is, should PREPROCESSING STEPS also be separately as well?) or does it not make any sense?