It's great you're here asking questions, because Rome is more enjoyable with some forward planning, let alone on the most busy weekend of the year! You're only in Rome 2 days?? Yikes. I see you're heading to Bologna from Rome, may I ask why only 2 days in Rome? Consider using the Time Shifter app to try to alleviate some jet lag symptoms. Normally you could go wait for a taxi at FCO, but arriving the day before GF, I would book through the hotel. It was 65 E last December. What time do you leave Easter Sunday for Bologna?
Schools are out across Europe from Maundy Thursday, so expect lots of families. I would absolutely book the Vatican Museum ahead of time if you can, don't rely on being there at dawn wasting time with others trying to get same day tickets. Here's an interesting link about avoiding the crush in the museums, if you're willing to go later in the day... https://www.romewise.com/visit-the-sistine-chapel.html
You mentioned getting out early, yes do get out as early as possible & at least take a walk to the Trevi Fountain & Piazza Navona, Rome is so much more than the bigger sites!
Opinions here are divided on the Coliseum, we are in the 'take a stroll at dusk and look at it from the outside' camp. There will be as many people saying you MUST see it. So if you don't get tickets, consider walking first to view the Forum, then down to the Coliseum - Walk up to the Capitoline museum for great views out over the forum, (Just continue straight past the museums and go right down the hill to the viewpoint.) We also walked up to the “Coffee Capitol” opened every day from 9:30 am to 6:30 pm for even better views over Forum. You can get there without entering the museum. Walk up the stairs to the Campidoglio, take an immediate right at the top, walk under the arch and to your left you will see the entrance. BUT it’s a LOT of steps by the time you get to the cafe. Then turn right coming back from viewing forum in the Capitoline square, leads down hill & stroll down the Foro Romano walking street to the Coliseum.
Take a look at meal planning - Personally, I don't like wandering around looking for places to eat once everyone is already hungry. Good Friday & Easter Sunday will see a lot of places closed, but not everywhere. Once you have the basics of your itinerary, look at the areas for good and or cheap eats. The Jewish Ghetto restaurants will be open until sundown on GF, (start of Shabbat) and open all day on Easter, but I would book ahead. One way to eat cheaper and have less of a crush is to eat out at lunch time & just grab pizzas by the slice for dinner. Or go to bakeries for both meals!
https://community.ricksteves.com/travel-forum/general-europe/jet-lag-i-tried-the-timeshifter-app - Info on Time Shifter app.
Good luck!
