You've done your homework! Good choices. A few comments.

1. It's good to see the Colosseum both during the day and at night. If at night, you really don't need to go all the way to it to see it. At night it's kind of a sketchy area. If you are going to a night tour, take a cab. Depending on what time it is, you'll have to walk back. I just don't know your travel style, and if you're the type who feels confident going anywhere. I don't have a problem, but for most, the immediate neighborhood of the Colosseum isn't all that comfortable. And, there's not much reason to go all the way to it, except during the day. Just as fascinating is the Forum at night (as well as during the day). The Colosseum and Forum are specularly lit up at night. You have to pass by the Forum to get to the Colosseum anyway, so you can go to the Forum at night, a nicer area, and see the Colosseum from there. It will save a lot of walking too.

2. Emma for pizza is great. I ate there in July on a spur of the moment decision. There were no tables, of course. They did finally find a place on a stool for me, standing up. You'll need a reservation. Ask the hotel to do it for you as you check in, if not before you leave the USA.

3. Cesare is a great choice. Make sure to have their fried appetizers. Reservations are a must. They are hard to do from the USA unless you can speak Italian and call them up, because you can't do it by email. Have your hotel do that. You can email your hotel and ask them to do that before you leave the USA. Just make sure they confirm it has been done. Also, I don't know when your dates are. A lot of restaurants are closed, for example on Monday. Others on a Wednesday. Check websites before hand, so that you can change restaurant dates accordingly, and don't get disappointed.

4. I never heard of Centro Storico Fountain. Do you mean Fountain of Trevi? That should also be seen both day and night. If you're staying near the Pantheon, it's just a 5-10 minute walk.

5. The catacombs, the one I'm thinking of, is quite a ways away, down Appian Way. I've walked there. It is a long hike, and would take up an afternoon. I wouldn't do it now. It's a long, long walk. On the way, you'd pass the Baths of Caracola, which is worth a look. Of course there are other catacombs you might be referring to, as even some churches have them, but the one on Appian Way is the one I think about when I hear catacomb.

6. You really have to see Piazza Navona, and it's best during the day. If you are going to walk to the Vatican, and a strong walker can, you will be able to walk through it. From the Pantheon, it's going the opposite direction from Fountain of Trevi. From there, a walk along the Tiber and then crossing over the San Angelo Bridge over to the Vatican is not a bad afternoon at all. Very scenic.

7. I don't know Tavernaccia. I try not to eat in Trastevere. It's become so, so touristy, and hard to eat there, but this place has a good reputation.

8. Pompeii, I would not consider at all during a 3 day vacation in Rome. That's overreaching. You'll spend your whole day traveling, be exhausted, and you'll miss a whole day of Rome. You can take an early train, actually several trains, and get back lat at night, but that's burning a day in Rome to sit in trains, or a tour bus. But if you are visiting Rome, stay there at least long enough to catch its vibes.

9. For most people, a half a day at the Vatican is enough, unless they are really into art. You can walk from opening to closing for seven straight days, and still not see everything. The advantage of a guide is to let them curate the experience for you, and guide you to the most important things. You'll also have to see St. Peter's Basilica, and that will eat up some time. If you are hungry, sort of behind the Vatican there is Pizzarium, Rome's most famous place for pizza. Then pretty much across the street is the Cipro train station, which you can take back to near your hotel, but Roman trains aren't for everyone, so you'll have to think about that. Or just take a cab back from there.

10. Rome souvenir shopping depends more on the recipient. It's a hassle to lug back wine that you could get in the USA. Balsamic Vinegar, you cannot get at Whole Foods. At least not the real stuff. And it might not travel that well. Real, "traditional" balsamic vinegar comes from Modena, a different part of Italy, and for maybe six ounces, it would cost $150 to $200. It would never, ever be put on a salad.

The industrial stuff you can get in restaurants in the USA and at Whole Foods is not real balsamic vinegar. And, balsamic vinegar is not popular in Italy. When a certain celebrity chef from the USA started using it on TV, tourists started expecting it, so they started making the cheap stuff and putting it in restaurants and shops. There is no such thing as italian dressing on a salad in Italy either. It is pretty much red wine vinegar and olive oil, and that's it. Salads are not a big thing in Italy. They are served at the end of the meal, to top it off. Balsamic vinegar of Modena, the real stuff, is too expensive to be a souvenir. I'm looking at my little flask on my counter top right now. I bought it about a year ago. I paid about $175 for four ounces. I had a half teaspoon on it just this afternoon because I have an upset stomach. A balsam means something for your health, not salad dressing. A little bit of it is also spread on meats, sometimes a few drops on vegetables, maybe a few drops in a minestrone, or a few drops on a slice of parmesan cheese, and it's also used as a syrup over gelato. But that's not a Roman thing. Only in Emilia-Romana, as in Modena, Parma, etc. Traditional balsamic vinegar is hard to find in Rome, even harder in the USA, and certainly not at Whole Foods.

I came back from Venice about five weeks ago to do some work in California. Someone there really did a lot of work for me, really inconveniencing herself. I brought her back a small, framed oil painting of Venice. The real thing, bought at an art store, painted by one of the artists who restore the masterpieces in the churches, but who like all of them, do some painting of their own on the side to supplement their income. It cost me 135 euros, not a fortune, but she appreciated the thought so much, that I have a friend for life. It's a real oil painting, not something out of a bin, and only maybe 6 X 8. For everyone else, I brought some biscotti. I only travel with a carry on, so there's only so much I can bring. But for the right person, what matters is the thought you put into it. This person had done so much for me that I literally walked from one end of Venice to the other to go to that small art gallery on my last night to get her a gift that will last her a lifetime. So for gifts, you're going to have to use creativity.

11. Other places you mention for lunch are good, but cacio e pepe is a long way from the Pantheon, for what seems like a routine place. When you say Antico Forno Roscioli, are you sure that's what you mean? There are three Rosciolis within a block or two of one another, down the street from Campo de Fiori. The famous one that is on all of the best restaurant guides is Salumeria Roscioli. You must have a reservation, but for lunch, sometimes you do not. In any case, the bar is first come first serve, and I've dropped by there for lunch on the spur of the moment quite a few times and gotten seated. Salumeria Roscioli is the famous one. Antico Forno Roscioli is around the corner, and is a bakery, but also noted for great pizza and sandwiches, so it is a viable lunch place, but it's almost sad to be in Rome and not eat at (Salumeria) Roscioli. Down the street is the Roscioli bakery. Mordi e Via is a good choice because you'll get to see the Testaccio Market, although I've heard they may have opened a second location closer to the historic center.

12. You can pay with a credit card at restaurants, but not at a bakery like Pan Divino, or Antico Forno Roscioli. You can, but they may or may not take it. You can't use it for street food like Mordi e Vai.

13. Table water is not free, and you shouldn't ask for tap water. It's clean enough, but it's running through aqueducts that are almost 2,000 years old. It's clean but not good enough to have with a meal. They will ask you what kind of water you want, and it's either frizzante/gassata, or naturale. Meaning bubbly, or still. Make your choice. Table water is not a rip off. It's also OK to say no water if you are going to drink something else. But asking for tap water does not present oneself well.

14. Some places have house wine, most do not. They'll all have some choices by the glass. For places like Roscioli and Cesare, the best thing to do is to ask the waiter to make a suggestion. At just any old touristy street place that won't do, but at a good restaurant, it's not a worry. In the USA, the more expensive the wine, the higher the bill, and the bigger the tip. In Italy the waiters are on salary and don't expect tips, so they have no reason to upsell you. Some of the wine pairings that have been suggested to me have been absolutely amazing, and completely change the pleasure of the meal and taste of the food. If going to a place of quality like Cesare, I'd always just ask the waiter what they recommend. They re professionals, and will take good care of you. I've never been upsold. It's part of their profession to tell you what would go well with a particular dish, and what is a good buy. For example, in July in Rome I had a mozzarella/burrata starter. i'd have never thought of drinking a moscato with that, but the waiter had me try that, and now there could never be anything else.

15. They will not switch the menu for tourists and give higher prices. Not if you are going to decent places. I mean, if you eat a you can just walk into near Fountain of Trevi, Spanish Steps, the Colosseum, the Pantheon, just any place you come across, or a place highly recommended by TripAdvisor, I guess that could happen. It would never happen at a decent place. Around the Fountain of Trevi they'll charge you 15 euros for fake gelato. At a decent place you will always need a reservation unless you are extremely lucky and there has just been a no-show. The places that require a reservation, which is all good restaurants would never, ever do that.