Please review my 7 nights in Tuscany Itinerary

Chiusi is not terribly interesting, except for its excellent Etruscan Museum. If you want to visit it, try to sign up in advance for the guided tour into some tombs. The tours are not done every day, and you need to reserve. Day 4 looks overcrowded to me.

The schedule you describe sounds exhausting if not impossible.
It sounds as if you wish to hit all these towns just to say you have been there. They are farther apart than the map would lead you to believe and will take more time to get to than you would imagine. Why not give more time to each place you visit to be able to enjoy them. We were in Tuscany and Umbria last fall and had a rental car. We stayed in Orvieto for three nights from which we drove to Cortona and Montepulciano. We spent a complete day in Orvieto. We allowed travel time to Volterra where we stayed three nights. We spent a complete day in Volterra and on another day drove to San Gimingnano and Pisa. Our last two nights were spent at an Agriturismo near Orvieto. One day was spent at the Agristurismo and another we drove to Todi. Then to an overnight stay at a hotel near the Rome airport for our next day flight back to the states. Skip Chiusi. We stopped there for about an hour and didn't find it worth while.

I'm of the 'seen one hill town you've seen em all' persuasion. Not really -- but as a caution to take a half day to enjoy, say Montepulciano and stay for dinner and then back rather than hitting three somewhat similar places in a day. e.g. Montepulciano, Pienza, Montalcino -- possible, but why? Mix it up with an abbey here, a garden there. I'd give Siena a full day and perhaps Volterra and San Gimignano another. There is a terrific Etruscan Museum in Volterra and San Gimignano is a good place for dinner in the evening when the tour buses have gone. Less is more and just enjoying the beauty of the countryside. Consider the gardens of La Foce and the Abbey of Monte Oliveto Maggiore or the Abbey Sant Antimo. The drives in these areas are stunning. You can see La Foce and just some of the countryside here. https://janettravels.wordpress.com/category/tuscany/

Give yourself some time to enjoy a picnic, a stroll, sipping wine on a terrace overlooking the Val' d'Orcia in Montepulciano etc etc. These towns are similar; being there rather than rushing here and there is likely to be more satisfying.

Since you're staying in one place and will have a car, I think it is great to have a general plan of what you want to see each day, but I would recommend that you keep it flexible. You might wake up one morning and just not feel like jumping in the car. You might be driving along some road and see a turnoff that looks interesting and decide on a whim to go that way and see what you discover. I've been to about half the towns you have on your list, and they're all worth seeing, but some of my favorite stops were spontaneous.

As for Viator, my understanding is they don't actually offer any tours themselves. They are just an easy and convenient way of finding what's available from third-party tour operators. I've booked some tours with Viator and never had a problem or issue. Sometimes they get a good deal with the tour operator and can offer a good price (and according to their web site, they offer a low price guarantee), but do some research and make sure you know what you're getting.

As for whether you need a tour for Florence? I wouldn't recommend it. You only have one day there, and there is so much to see. You'll want to do it at your pace. You can easily read about everything in the guidebooks or follow one of Rick's walking tour podcasts.

Sounds like a great trip! Enjoy!

This grouping may work better ...

Day 2: Drive to Montepulciano, Pienza, Montalcino (probably not all 3)
Day 3: Drive to Volterra and San Gimignano
Day 4: Train from Chiusi to Siena
Day 5: Drive to Cortona and Arezzo
Day 6: Train from Chiusi to Florence
Day 7: Drive to Assisi