How to get a list of all available iControl APIs and its documentation

The API and the GUI are two separate and independent things, one does not directly map to the other. This shouldn't matter as where the API is concerned things are named in a fairly logical way and it doesn't take too much effort to find what you're looking for in most cases.

The only documentation available as far as I'm aware is what is available on DevCentral, in particular the iControl wiki.

As to what the API is for, what is any API for? Sorry to sound unhelpful but hopefully you'll gain a better understanding doing some research.