William Saroyan had this to say about the visual arts: "Art is looking at things carefully." I'd like to add that literature is "the imitation of an action by language" (Aristotle calls it "poetry" and divides it into three kinds, depending on the number of narrators). When a writer takes great care to describe a mis-en-scene, or to depict a character's complexities, or to articulate an abstraction, it is art -- as opposed to "commodity," a distinction first explored in Elizabethan times, and blurred today by the ever-present free enterprise system.
Literature and the other fine arts are all similiar in that they are specific media through which one gives expression to what is in the soul. For instance, poetry is often set to music or dance interprets music, art imitates literary form. All of the fine artas attempt to solidify, communicate, and embellish thoughts and comunicate in a manner that transcends all others.
Each of the things you mention is a method by which creativity happens and human nature can be reflected. They're connected in that they require someone with a point of view to create from a particular perspective. They're similar because they have the ability to elicit a response from those who experience the creation. They're all art.
Literature can help to inspire other mediums of artistic expression. Challenging and powerful literature can set the stage for amazingly poweful and compelling representation in other forms. For example, Picasso's rendering of "Don Quixote" raises as many thought provoking discussions as Cervantes' work, itself. However, there are times when literature cannot seem to make the jump from its pages to other mediums. I am not sure why this is, but there are times when literature cannot be replicated into other mediums. Having said this, perhaps the relationship between literature and other mediums is that they can both be used to articulate experiences within the human predicament. They might be able to serve vehicles that express the level of "truths" that we endure and seek to voice.
I tend to think that all of these arts are a response to the culture and events of particular time periods. Though literature may not be directly affected by another type of artistic movement, both are affected by history. For example, when you looked at Modernist literature (Early 20th century) and compare that to the other arts, certain themes pop up: the need for the individual to express himself or herself in an increasingly more chaotic world, an experimentation with or even rejection of certain traditional elements, etc. For example, compare and contrast the movie Metropolis (directed by Fritz Lang in 1927) with The Trial (1925) by Franz Kafka, you see two completely seperate works that both deal with the fear of dystopia and the complete extermination of individual free will. Considering both of these were created post World War I by German artists who would have reason to fear a crumbling society, this feeling certainly makes sense.
Literature, like the other arts you mention, is an expression of individual thought and feeling achieved through the creative process. Artists seek to share their experiences, observations, and understanding (their "truths") through the medium that most effectively lends itself to their personal skills and abilities. Whether artists are writing stories, painting pictures, writing music, composing a photograph, or creating a film, they are expressing their relationship to the world around them at that moment. Their works share certain expressive elements, such as structure, theme, and tone. Art connects human beings to each other in that it allows us to share each other's perceptions, emotions, and experiences. A gifted artist may capture creatively what we feel but cannot express ourselves.