Finalizing my first solo trip to Italy/Dublin. Need help for Rome

Don't worry about the Spanish Steps and Trevi Fountain, they are outdoors so they never close. If your hotel is near the Pantheon it will be very close to Trevi/Steps. The Victor Emmanuel is also very close, should have no problem walking and it doesn't close for the afternoon.
After the Vatican tour, climb the dome.
Try to do the Churches on Friday. I'm not sure about visiting on Sunday Morning because of Mass schedules. Take a bus (on the Via del Corso) or cab to San Giovanni first because it is the furthest, and work your way back to St. Peter in Chains then Maria Maggiore. (I don't remember what times we were there, but they always seemed to be open.) Just plan on eating during closing times. We did these 3 Churches plus St. Paul Outside the wall in one day with no problem. You should be able to do your three.
Before your colosseum tour, consider the Capitoline Museum. The staircase up to the piazza/museum is the second one to the left while you are looking at the V.E. monument.

Don't panic, a hotel near the Pantheon is almost dead center in the city which makes it easy to walk just about everywhere. We did take the bus on the Via del Corso to the Vatican three mornings (to save our feet some steps for the 4 hour tour) and it is a very short ride. We walked back each time using a different route.
I have to think a little bit more.......

There are 3 Alilaguna lines to San Marco, Orange, Blue and Red. The Red Line doesn't start operating again until April so there's no timetable available yet. They all leave from the same place. The Orange and Blue take about the same amount of time to get to San Marco, so you'd take the next one to leave. When you enter the airport terminal there's a transportation booth almost right in front of you where you can buy a ticket.

Buy your ticket from Assisi to Rome in Florence when you buy the ticket to Assisi. Don't forget to validate your ticket in one of the new green or old yellow machines before boarding. When you get to Assisi, you may want to leave most of your luggage at the station and just take a small overnight bag up to the town. Most of Assisi is steep up and down, some streets are so steep they have stairs. I was in Assisi in mid-May 3 years ago and there weren't any crowds.

First, congratulations on doing so much planning and research. You are better prepared than 99% of visitors, so don't worry - you'll have a great trip.

Don't be scared about Rome. Not only are you in a central hotel, but by the time you get to Rome you will already have had over a week in Italy, so you'll be used to how things work. You can ask about bus routes at your hotel, and if you want a taxi, they'll point you to the nearest taxi rank, which will be very close by. Taxis don't cruise around in Italy; you either go to a rank or call one. If you call one, the meter starts when they get your call, so the taxi arrives with some extra euros already on the meter; this is normal and not a scam. In central Rome, taxi ranks are all over

And once you're there, you'll indeed see that when things close for their midday break, that's when you will be eating lunch. Lunch in Italy is not a rushed affair. While there are certainly things, including larger stores, open during the lunch break (often indicated by a sign with some variant of the words "Orari nonstop"), at least once you should go with the midday break and do nothing more during that time than have lunch and a walk. Particularly in Rome, you'll really get the feel of the city that way.