I generally italicize/embolden punctuation as well. This is something you should discuss with the editor of the text because it can get weird with lots of quotations or complex citation system.

It depends on context and meaning. For example, there is difference between:
Should I emphasise everything? – and – Should I emphasise everything?

I meant rather something like the second example. In this case should I emphasise also the comma?

I emphasised everything, but I wasn't sure.
I emphasised everything, but I wasn't sure.

I've learned to italicize the punctuation mark - not because it is a crucial part of the emphasis but because it shouldn't draw attention to itself (like your second comma example does). I'll obviously reconsider if italicizing draws more attention to it.

I meant rather something like the second example. In this case should I emphasise also the comma?

Strictly speaking, no: the comma is not part of the expression getting emphasis, but rather a structural element of the entire sentence. However, in some instances an italic comma will fit better than a Roman one so, aesthetically, using the italic comma might look better. If the project is not academic in nature, I would go with what looks best, rules be damned...