I’ve traveled extensively through Europe using trains and it is a great way to travel.
It’s only an 8 hour trip from Rome to Zermatt so you’ll do it easily.
The times you have listed are fine and the connections are at the same station. The only potential issue you may have is if a train runs late. There’s usually plenty of others though.
Keep in mind quite a lot of trains in Europe require a seat reservation on top of the ticket price and the seat reservations are not transferable. So, if you miss the train you’ll have to buy another reservation.
Just make sure you catch the fast trains rather than the regional ones though.
Zermatt is a beautiful place, one of our favourites.
Enjoy!
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