Ciao Krisp!
As the others have already recommended and as you've already planned, take train between Rome and Montepulciano, then have the car for the 5 days in Tuscany, then take train back down.
Shopping near Montepulciano - yep, head to the Valdichiana outlets but also enjoy exploring and buying from the small shops in the villages you visit.
From Montepulciano, you can see a lot of southern Tuscany and get a feel for all the beauty that is here: visit Montepulciano, Pienza, San Quirico d'Orcia and Montalcino in that immediate area, then head to Cortona and Arezzo for another day, to Siena for another full day and another day to San Gimignano, stopping along the way in Monteriggioni and Colle Val d'Elsa. Not sure if you'll have the time but a day in Florence would also be suggested, if you can make it (the A1 from Montepulciano is the fastest way to go).
Many shops close during lunch time from 1pm to 3pm on average, meal times are from 12-2pm and from 7-11pm. You'll be able to eat out of those time at the small panini shops and "bars" (coffee shops) that have snacks as well.
Do wine tastings where you see the opportunity in the towns - they are all wine regions so have wine shops that offer tastings... and as you drive you'll also see signs for wineries. Stop if you can ;-). If you prefer to try a "tour" for the wineries so you don't have to drive, take a look at the many offerings listed here:
http://www.partner.viator.com/en/8357/
Wine tastings here can be pretty low cost, from 5-10 euros depending on how many wines. Then if you add tastings of other products or lunch then price goes up but in general, cost is low.
Since you'll be in the area, take a look at the tastings offered near Arezzo here as part of the "Giorni del Vino" here:
http://www.discovertuscany.com/arezzo/what-to-do/i-giorni-del-vino.html