What a confusion you are elaborating:
1. The Villa in Sintra does not belong to Fundação da Casa de Bragança.
As far as I know there are none or very few relations between HRH and the Fundação.
Don't forget that Salazar "nationalized" the properties of the Bragança Saxe-Coburgs after D.Manuel II's death, depriving the Bragança branch of what they historically considered to belong to them.
And still today the relation is rather tense.
The house of Sintra belongs to D.Duarte himself.
It belonged to an old monarchic friend who was childless and was thinking of taking exile in Brazil after the 1974 revolution.
Therefore he offered the Manor to D.Duarte for a very cheap price.
Mind you, the ancient owner did not want the House occupied and vandalized as so many were at the time, he was in a hurry to leave, he knew D.Duarte was not a very wealthy man and as a good monarchic he preferred to sell it cheaper to someone who would respect the house.
The fact that the house was so cheap also reflects that it was not in a very good shape, Sintra being a very damp micro-climate area.
I know what I am talking about, I have a summer house in the neighbourhood
When D.Duarte got married, a group of friends joined in and their present was a partial renovation of the house, roofs, pipes, paint, etc.
After all, it would be no longer a bachelor's "pied-à-terre", but the home of the future RF, with a wife and kids, and D.Duarte would have to receive and entertain more.
2. The House in Ferragudo, Algarve was left in inheritance to D.Duarte by his aunt Infanta D.Filipa, who lived the last years of her life there and died in the very same house.
I heard that it used to belong to one of Infanta D.Antónia's sons who left it or sold it to his aunt D.Filipa but I could not confirm the story.
3. The third property D.Duarte owns is Casa das Fidalgas in Santar.
It is ran by Infante D.Miguel who lives there most of the year.
I didn't know it was opened to the public.
This weekend I will be in that area, so I will try to pop in.
EX LIBRIS: CASA DAS FIDALGAS EM SANTAR
Nearby is the reputed Quinta da Viscondessa de Santar, famous for its wine cellars and lovely gardens.