By Tatooine, you mean a planet with two stars. According to scientists, such a planet like Tatooine from Star Wars could exist and scientists believe they have found one. The planet has the rather boring name of Kepler 47b meaning its the second planet out. The star system also has another planet called Kepler 47c.
The furthest galaxy from here is UDFj-39546284, rather catchy name don't you think? According to scientists, when we look at the galaxy, we are looking at it as it was 13.2 billion years ago, that is a mere 5-600 million years after the big bang. It is smaller than our own Milky Way galaxy and is one of many mini-galaxies in the universe. There could be a galaxy further away but its light would not have reached us yet so we don't know about it.