The horse The Evil Queen rides is called Rocinante. That is the name of Don Quixote's horse. It is also the name of the ship in "The Expanse." The name translates loosely as "best old nag."
The object/animal/person in this episode are Enchanted Branches.
Regina says of their new world that of all the worlds it is the "fairest of them all." This of course is the same phrase from the film Snow White and the Seven Dwarfs (1937) that the Evil Queen says into the Magic Mirror: "Mirror, mirror on the wall, who's the fairest of them all." The answer that came back of course was "Snow White."
Robert Carlyle improvised Rumplestiltskin's sing-song line, "If you let me show you how."
When Prince Charming pulls Jefferson out of his vehicle, there is a box with a Deluxe Tea Set outside the vehicle.