Transfer at FCO from Terminal 1 to 3

I have a total of one hour and 30 minutes to get to terminal 1 once l've left Terminal 3 with my luggage.

Not sure how you calculated that since your flight departs 2.5 hours after your scheduled landing. But if your number is right it might be tight. ITA has smaller planes (737 size) and typically they are parked out on the tarmac and you take a bus from the terminal to the plane, meaning you need to be at the departure gate a bit earlier than when the plane is parked right there.

Why do you need to check baggage if it's carry-on for Delta? Both Delta and ITA let you carry on 1 piece of luggage meeting size and weight requirements plus a personal item. The weight limit for ITA is probably tighter than for Delta, though, but I didn't see them weighing any bags (which isn't to say they can't/won't).

As for check-in, I put the ITA app on my phone and used it to check in (I had been in Italy for a few days at the time of my flight). ITA lets you check in online 48 hours before the flight so you can do that at home prior to your flight to Rome and either print a boarding pass or verify it shows up in the app on your phone.

Lastly, for advice. I don't like your plan. There are later ITA flights and I'd rather be bored sitting in an airport for a few hours than stressed realizing I'm in Rome with no way to get to Sicily that day because the flights are full and I missed the one I was booked on. When I was flying back from the RS tour in Sicily last year I flew to Rome, spent the nite, then flew home the next morning. Stress free.

This would make me incredibly nervous. Could you not buy a ticket to get you all the way to Palermo? We flew Delta to Catania and the leg Rome to Catania was a codeshare with ITA. I don't know what to suggest. Can you take an earlier Delta flight to give you more time in Rome to make the transfer? You actually have two hours and 30 minutes, unless I'm not understanding something. Still, you would want everything to go right, maybe even your Delta flight getting to Rome early.

It is enough time if you are very lucky. Immigration (passport control) is going to be your problem -- not customs. I would get seat a seat on the Delta flight as close as you can to the deplaning door. Try as hard as can to be one of the first off. Walk fast to immigration and hope that there is not much of a line. If there is, ask one of the attendants if you can jump the line because of a very short connection. Sometime there will be special line for short connections. I have taken as long as 3hrs to get through immigration in Rome although it is often closer to 30, 45 minutes. Customs is a walk through the green door -- nothing to declare. Walk as fast as you can to Terminal 1. Find the ITA desk and check-in. And, of course, you have to go through security -- again!!! This assumes you have carry on luggage only. Sometimes the desk will close 30 minutes or so prior to boarding so hopefully you can make it by 9.15. And your flight absolutely has to be on time if not a little early. If you have to wait for checked luggage on Delta you cannot make it. Sorry.

You will need a plan B. Good luck and you will need it.

I went through a similar sequence this year, American to ITA to Palermo, and would have successfully made it on your schedule. But - any chance you can exchange your ticket for a slightly later flight to Palermo? There are so many of them. i wound up kicking around Terminal 1 for quite a while, but at least I wasn't worried about making a connection.

I would think you can check in for your ITA flight online before you leave the US. Then you just need to drop off the bag if they won’t let you take it on since it may be a basic economy type of separate ticket that you purchased