External parts of the house that is shown in the movie is the house where Rudyard Kipling was born. The stuffed tiger toy in the movie is called Khan and the book the mother keeps reading to her son is Jungle Book. Probably the maker's way of paying tribute to Kipling.
Myrtu is played by Javier Botet. This is not the first time that Botet plays a horror girl, since then he played Niña Medeiros in the [Rec] (2007)'s franchise as well as the feminine ghost in Mama (2013), and most recently as the Crooked Man in The Conjuring 2 (2016).
Myrtu is named after the Sanskrit word "mrti" which means "death". The god of death in Hinduism is Yama, sometimes identified with Kala, god of time, as time consumes everything and finally brings death. Shiva is a male deity; he presides destruction which allows for new creation by Brahma.
The trivia items below may give away important plot points.
The movie addresses about a Hindi men called the Aghori. In India, Aghori is a real sect born from a tribe called Kapalika, and separated from this last one since the 14th Century. The Aghori are known to practice necro-cannibalism (devouring those corpses thrown to the river Ganges, instead to be incinerated following the traditional mortuary rituals), in the belief that eat flesh from dead people will bring special powers as stop aging and other physical benefits. Although they are rejected from the Hinduist religion, in the rural zones from the country they are considered powerful medicine man, capable to heal to sick people by their knowledge about human body. Usually Aghori don't have dressed, standing nude, dressing with clothes from dead people or full-covered with the ashes from the bodies cremated.
When Maria travels in train, she takes a little red ball to bring back to a little girl from the next seat. in The Changeling (1980), John Russell (George C. Scott) is haunted with a little red ball thrown by the upstairs of his house.
When Piki tries to burn Oliver's belongings, the spirit of her daughter Anushka emerges from the waters of a little artificial pond. In Mama (2013), the spirit of a woman emerges from a pond invoked by Annabel (Jessica Chastain) to recover her kidnapped daughter.