Train vs. hired car Cinque Terre to Arezzo

First of all Pisa is spelled with a "s" not with a "z".
Answers to your questions:
1. Yes
2. Very
3. Don't make reservations, your trip will be on Regional trains (except for maybe the La Spezia to Pisa portion, which have intercity and Frecciabianca service). Just buy the tickets at the Vernazza station on the day of departure (don't forget to validate the ticket before boarding at the stamping machine on the platform).

You can stop and visit Pisa along the way also with the train. Just deposit your luggage at the luggage storage at the station.

After answering your questions above, I would give you additional advice.
If you are renting a villa NEAR Arezzo, chances are the villa might be an Agriturismo (farmhouse) in the middle of the countryside where public transport is infrequent or non existent.
I recommend that you rent a car instead for your Arezzo staying. In that case I would rent a car in La Spezia (near Vernazza) and drive to your villa near Arezzo from there (all freeway driving).

To add to Roberto's advice?

There aren't really any first-class tickets for regionale trains as there are no reserved seats on those; they're used mainly for shorter hops, and tickets are inexpensive. But even on the trains which do require reservations, we've always traveled 2nd class - unless we run into a good deal on first-class tickets - and haven't minded those carriages at all.

I would not be concerned about the short transfer time in Pisa. Since you're planning for it, you can be ready to hop off the train right when it stops. But I'd share Roberto's concern that you might really need/want a car if staying at a rural agriturismo.

Thanks for the advice that the train is the way to go. We do have a car rented in Arezzo to have available while at the villa as well as private guide for two separate days to local towns & wineries.
Ciao!