My husband and I have been to Lisbon twice in the past two years so I will try to give you some specific answers to your questions. Overall, you have a wonderful itinerary for a first time visit. The only thing that I see that is missing is seeing a Fado performance. You can do that over one of your dinners. Lisbon is the birthplace of Fado and if you haven't seen a performance before, it is a magical experience.
Day 2: I have taken the Rick Steve's Baixa and Barrio Alto self-guided walking tours my first time to Lisbon in 2023. Each tour individually takes about 2 hours, assuming you don't make too many stops along the way. The big open question in the walking tour guidelines is whether the Gloria funicular will be open (tentative for April). They were offering bus replacement service, so check on that alternative. If that is not available, then you can use the Rossio train station escalators to get you partially up to the Barrio Alto, but then you have to walk uphill from there (we did that in September 2026 and I don't recall it being too strenuous).
A note on the Barrio Alto portion of the walk. We stayed in the Barrio Alto on our trip and spent a lot of time exploring the areas that RS outlines in the book.
When you visit the Miradouro de Sao Pedro de Alcantara, there is a little cafe that serves my favorite drink in Portugal, the Port Tonic (white port and tonic over ice). Since you will have been on your feet for awhile on the walk, this is a great place to sit down and have drink (super casual). The other stop that you may want to have a drink is the roof top bar behind the Carmo Monastery. It has a wonderful view of the city.
Since you are going to be in the Barrio Alto in the day, I can recommend a few restaurants for lunch. Leve Leve: https://levelevetapasbar.pt/ great for tapas style meals, chicken skewers are amazing as is the honeymoon goat cheese. Taberna Carolina tucked away beneath the Church of the Martyrs see story here: https://www.eatingeurope.com/blog/taberna-carolina/. Taberna Carolina has awesome caldo verde (potato/kale soup topped with sausage). It is located near Livraria Bertrand the oldest operating bookstore in the world (stop by here and by a souvenir book and have them emboss it either in English or Portuguese). Cafe A Brazileira has been in business since 1905 and is well positioned for people watching. It is touristy and there can be a wait, but they have the most amazing French toast.
Oficio is my absolute favorite restaurant in Lisbon. It is dinner only. Since the Michelin guide has recognized them, it is challenging to get a reservation, but the food is so inventive, tasty, and stunningly beautiful. Great wine list and attentive service.
Day 3: Sintra tour, one tip is to minimize the strain on your knees, tell the guide you want to take the little tram up instead of walking up. They should offer it, but if not ask.
Day 4: Belem. The highlight for my visit to Belem was the Jerónimos Monastery. Book tickets online for a designated time. After Belem when you visit the Castle would recommend that you book in advance as they lines can be long. We visited the Castle and honesty we wished we had not wasted our time, so if you have a time crunch, I would skip visiting the Castle and just do the walk.
Day 5: Staying in Lisbon versus staying near the airport. Each time we visited we had a very early morning flight and the airport is so close to town that you can get an Uber and be there quickly enough. We opted to do that and were glad as we had time for one last evening in Lisbon to enjoy. We knew that if we stayed at the airport, we were unlikely to go back into Lisbon for dinner.