You can use contactless payment for the metro - we did it a couple of months back. It's possible some stations don't have it yet, but we didn't run into any, staying mostly in the core of Rome. Cavour, Vittorio Emanuele, Piramide, Cipro are the ones I specifically recall having contactless payment right on the entry turnstile. Apple watch, apple pay, and a contactless card all worked for my family. Busses might be hit or miss, we didn't ride any this past trip. For trains, the ticket kiosks take cards and contactless mostly. Getting to/from FCO via transit requires you to purchase a train ticket online or at a kiosk. Look on the Trenitalia website for timetables and advance purchases if you want that, or you can get them at the station. Both Termini and Fiumicino stations have ticketing kiosks that take cards.

With cash, you should still carry some. Smaller purchases like a coffee, yeah, use cash if you can help it. For larger shopping trips like groceries, clothes, etc, credit cards are fine. Amex is not accepted everywhere though, so bring a Visa/MC just in case. My personal guideline is to use cash for food without service, and small purchases under ~10 euro. Card for everything else.

I have T-Mobile Magenta Max and it was great. Definitely sufficient for a week long trip if my family is any indicator. The data speeds were very fast. You may want to load up WhatsApp, since some businesses use that for texting things like reservations and takeout orders, if you don't want to call them. But lately it seems like many have moved to online reservation tools, and the rest are responsive over email. Some you just need to call, though, and your T-Mobile plan will work just fine for that. Our most recent trip was the first time I'd not even bothered to switch to the TIM SIM that I keep active - I'll probably let it expire, in fact.

My other unsolicited suggestion would be to load up the Uber app - it's all Uber Black in Rome, but vans for larger groups/families tend to be fairly inexpensive compared to the US. FreeNow is also a good app for hailing regular taxis. Depending on where you're going, this will be a lot more convenient than transit.