Trenitalia has an app that will store the tickets, check track details and also let you track any trains for connections if you have them. I have heard that for some weird reason it is not available in Canada so you might have to wait until you're local to download it but I recommend it.
If you have the tickets in the app and you click "check in" for fast trains after you're sitting in your seats and then train is moving they usually won't even ask for your ticket since the conductor can see you got on the correct station, are in your seat, and have checked in. Then you won't even need to show them to the conductor. But ditto on being paranoid and making a screenshot of the tickets just in case. I've never needed it but you never know when you might not have cell data when when you need it.
In Bologna the fast trains leave from Level -4 and take an airport type transfer via a series of escalators to get to. So arrive early when you leave and don't hang around. If it's a fast train you know it leaves from the lower levels so you can head down even if you don't have a track assigned yet. All other stations are laid you flat and are more straightforward to use even if super busy.
Have a great trip,
=Tod