Hi everyone
We're picking up a car from Rome Termini and driving to Abruzzo (Sulmona) for a few days. Can I avoid the ZTL's while leaving and returning to Rome

Of course you can, do not drive past this sign. As easy not driving past this sign or walking past this one.

Absolutely. Picking up and depositing a rental - I've driven into and out of Rome without hitting one of those dreaded ZTLs many times. You'll be fine.

Ask the rental agency to point you in the right direction. The rental agencies at Termini station are outside the ZTL. Basically, if you head north you won't hit one. There is often very heavy traffic in that area. I myself would prefer to pick up at the airport.

Search :"ZtL" in forum and read the "interesting" stories that will answer your question.

We parked our car in front of our apt to leave Florence, I stayed with the car, hubby got the bags. It was in a zone so six month later we got a ticket in the mail. How we could have avoided it I don't know. We were in italy for 2 months so had more luggage than usual.

If you want an exemption to unload (or reload) luggage, your hotel, apartment, or B&B has to request this permit from the local police. The permission will be for a specific time window, and in some cities, you have to follow a specific route to get there. You should have asked your apartment rental agency about this in advance.

Some apartments are rented under the table to avoid taxes, and if your apartment is one of these, the owner is unlikely to be willing to request this permit. In that case, you have to keep your car away from the ZTL and arrive there by bus or taxi.

Here is a good article about ZTLs and how to avoid fines.
https://www.autoeurope.co.uk/travel-blog/driving-in-italy-what-are-ztls-and-how-to-avoid-them/

I would just caution that not every city allows permits for the duration of your stay. Always ask your hotel.
Even people who live in Italy, as we do, sometimes stray into a ZTL. Once, in a city we know well, we got caught because they had recently changed the zone, and we were so sure that we knew where we were going that we weren't looking for a sign. Luckily we were stopped by a policeman instead of caught by a camera. He took pity on us because of the recent change.

Another time, in Bologna, we followed a bus into a ZTL. The bus blocked the sign from our view. Fortunately, it apparently also blocked our car from the camera, because the ticket never arrived.

I read about a nurse who got a job in a new hospital and unknowingly drove through a ZTL twice a day for months before the tickets started to arrive.