What would be the best way to add a Google Advertisement after every 3 articles in a category display?

You would have to write a custom plugin to do so, that counts the K2 items generated then adds in the code.
Or, you could manually add this, but then you are open to the possibility to forget to add the code.

The Category List view as default, we just display either all the content from within that category or also from all sub categories from with that category, depending on how you set the catalog mode.

Hope that helps a little.

Simon
K2 Support