The music that Francisca and her father dance to is "Naufrágio" in the voice of Amália Rodrigues. This type of Portuguese traditional music is called "fado", which translates to "sad destiny", and it's commonly used to express the feeling of losing someone dear.
The three Portuguese-speaking actors all use different accents: Lucy (Flora Diaz) has a Brazilian accent, Francisca (Kika Magalhaes) has a continental Portuguese accent and António (Joey Curtis-Green) has an Azorean accent.
The movie that is playing on TV in front of which a grownup Antonio is seen playing is William Castle's House on Haunted Hill (1959). The voice heard is that of Vincent Price.
Writer/director Nicolas Pesce's mother dissected a cow's eye with Pesce just like Francisca's mother does with Francisca in the film.
The show that Francisca's father keeps watching on TV is Bonanza (1959) that was aired from 1959 to 1973. The particular episode (S01E26) that is featured in the film is titled The Avenger.