I think your Friday is going to be very full of both historic sites and walking. Over the course of a number of visits to Rome, we've only visited the Palatine Hill once (and the Forum and Coloseum almost every time). The Palatine Hill is more ruinous, so it's more difficult to envision how is must have looked. You may enter information overload after the Forum, Coloseum and the Palatine Hill.
For lunch in that area, we like Hostaria Isidoro. Lots of good pasta choices (and other foods).
It will likely be late afternoon once you finish those visit. Also in the area, and very interesting, is San Clemente, a church bult on top of an older church, built on a Mithraic Temple, on top of an ancient Roman home, all available for viewing.
To walk from there to the Trevi Fountain, then to the Spanish Steps, and then to Piazza del Popolo is quite a bit of walking. You may just want to walk over to the Trevi, then down to the Pantheon or Piazza Navona and spend some much-needed rest time at a cafe, and visit the Piazza del Popolo. Which I have never found terribly interesting, BTW.
Your son may already have specific architecture books about Rome. If not, he might want to get the Blue Guide to Rome. Heavy and dense, but lots of detailed information on just about every historic thing in the city.
You might want to check out a company called Hands on Travel. They organize tours for the deaf, but it was started by a Deaf American with Italian roots, who now lives in Rome, and they have consultation services. While I think you would do just fine with your own guidebooks (that's how we visit places 90% of the time), they may be able to propose ASL guided tours in Rome, if you want to do that.
Enjoy!
