Rome

I will give you my personal opinion, but adapt them to your own taste.

• I would stay 4-5 nights - it's about the longest I want to stay in any city unless I move in to live like a local.
• HOHO is a very good way to get an overview of a city you haven't visited before. I recommend it.
• Trastevere is a nice place to live. Termini is only if you want to catch a very early train.

Others will give you other opinions. Choose your own :-)

I like the Pantheon/Piazza Navona/Campo dei Fiori area.

How many day do you recommend to stay.

It depends on how interested you are in what the city has to offer. I've spent nearly two weeks in Rome over the course of several trips, and feel as if I've merely scratched the surface. A week would not be too long for me but may be for you.

It is a good idea Hop on Hop off, we need to book online or in Rome
where to buy?

I'm not personally a fan of Rome hohos as tourists report too many negative issues with them, they can't get you directly to attractions in pedestrianized areas, can get stuck in traffic, and they're too big to get into the more interesting corners. If one has mobility issues, then they're an option to save a few steps but otherwise walking and occasionally hopping public transit is a more enjoyable and efficient way to see this city.

Vatican and sestene Chapel need to book in advance and is better to do
it in two days so is more enjoyable.

Yes, you absolutely should book reservations in advance as it will be mobbed in June and ticket queues will be very long. The Sistine is inside the museums so no, you do not want to split your visit.

Do you know if we can have the above tour with a guide so we
understand what we are seeing

Yes, you can pre-book a tour on the Vatican's website. I might recommend the 3-hour tour that includes St Peter's so that you can enter the church directly from the Sistine (only allowed for tour groups) instead of having to go 'round to a separate entrance and stand in security check queue for the basilica. You can do that here (see "Vatican Museums and St Peter's Basilica"):

https://biglietteriamusei.vatican.va/musei/tickets/do?action=booking&codiceLivelloVisita=4&step=1

Which area is good,everybody say that termini is not nice

We've stayed within a short-ish walk - roughly in the Repubblica neighborhood - of Termini and didn't find the location objectionable at all but everyone's preferences are different. There are few wrong answers other than staying so far out of the city center that it's time-consuming to return to the hotel during the day for forgotten items, a short rest-up or other need.

Four to five nights should be sufficient. That will include time for a half day trip to Ostia Antica. Check out the Rick Steves guide book for Rome -- it's a great resource and I think you can still get a small one that just deals with Rome itself.

Is Rome your only stop?

I agree with others that 4-5 nights would be great, but for a trip I prefer closer to 10 days, So I would be adding nights other places.

I too find the HOHO buses in Rome to be less than useful. The central core of Rome is mostly Pedestrian, so the bus drops you off blocks away from the sights, and even adding in the Vatican and the Colosseum, all are easily walk able.

Everyone has their preferences for where to stay, Staying down in the core (Campo di Fiori/Pantheon area) is nice in that so many things are just out your door, many prefer the Termini and Republica area...though it never appealed to me. I prefer the Trasteveri.

Yes, make your reservation for the Vatican Museum, which includes the Sistine Chapel. If you can afford a guide, that is a great option, if not there are some podcasts/audio tours that help. If you are concerned about a long day, do the Museum one day, then St.Peters, the Crypts, and climb the dome the next...no reservations needed for those. You can also attempt to get tickets for the Scavi tour, under St. Peters, that would be a separate effort through the Vatican website.

I would recommend 4 nights or 5 nights (3 or 4 complete days). I would also recommend a guide for two of those days. You will get the highlights (just tell them what you want to see (we chose ancient Rome, medieval Rome, Christian Rome, Renaissance Rome) and get easy access to places like the Borghese and Vatican. You will then have a day or two to do whatever you want in the rest of Rome you haven't seen yet.