You may not ask for a review which would be very time consuming. See this way, the professor would be receiving numerous applications from all around the globe and you are probably one among many. Think of him getting review requests from all of them (which would be statistically less probable by the way). He would be probably busy with his own research work and its more or less an annoyance if you ask for a review.
Now, if you are called for an interview or a presentation by the selection committee and if that requires preparation of topics specific to your potential advisor's research area, then its perfectly fine to ask him questions or suggestions for improving your presentation. Even here, I do not recommend you to ask for a review rather you may request for suggestions.
In Italy this would not be a problem, but I want to avoid to hit a cultural difference.
I don't think this has anything to do with cultural difference, professors are ought to be equally busy in both of the countries.