"We also see that it is recommended to contact the first hotel we will be staying at with the tour to see if they will extend us the RS rate for the days ahead so we'll plan to do that."
Yes, e-mail them directly, explaining that your are on a Rick Steves tour. And do this as soon as you are sure of your plans, since rooms at the RS Tour hotel are not guaranteed.
"How difficult/easy is it to get from FCO to the RS hotel in Rome? Should we consider a car service as first timers?"
It's not difficult and there are many ways. For first timers and with two people, I think the best ways are either an official taxi from the taxi line at FCO, or a pre-booked car service.
"Renting a car in Sardinia (Italy). Do we need to have anything more than our US driver's license and passport? I see a reference to an international driver's permit? Is this really needed? (Apologies if this info is listed on the website already.)"
Yes, an IDP is legally required. Sometimes it is required at the rental counter, sometimes it is not. But if you are stopped by police for any reason (including a checkpoint where you have done nothing wrong), you'll need it. It is obtained from AAA even if you're not a member, and is good for a year, which can start on any day you choose.
"It also looks like Italy takes speeding very seriously so I assume I shouldn't employ the DFW lead foot driving strategy. "
It's not just that they "take it seriously." Your speed is often monitored by cameras, so if your more than a very slight amount over the limit, it triggers an automatic ticket, that arrives with a picture of your license place. In addition to the standard speed cameras (that measure your speed at a particular point), they also use the Tutor system in places. This captures how long it took you to get from point A to point B; if it's faster than the speed limit allows, you are ticketed for speeding, even if you were not speeding at point A or point B itself. For instance, suppose the speed limit is 80 kilometers per hour, and it's 20 km from point A to B. If you get from A to B in less than 15 minutes, the Tutor system will issue you a ticket for speeding.
Note also that tickets come in two installments. First, there's a fee from your rental company, for turning over your information to the authorities (about €45 euros). You agree to this fee as part of your rental car agreement. Then, many months (sometimes a full year) later, there's the ticket itself.
There are also tickets for driving in bus lanes, and for driving into ZTLs (zono traffio limitato) - areas where cars without permits (that's you) are not allowed. So, start learning the rules now, so you won't be one of the people who come back here and post about how they got lots of tickets "unfairly," for not knowing or following the rules.