Good API must be Lazy.
Work like we are seeing before, similarity. Should look like the same. Principle of similarity. User should automatically guess how it work. It's about naming things, methods and functions. Reuse same patterns everywhere for the same purpose. Everything should look obvious for the user.
One exception, sometime, API should look ugly, very dangerous when something we do/should not want to use it because we should be afraid. Risky function should have risky name to represent them
People need documentation because they will probably do really complicated things with your API. One line of good documentation well placed can save hours to your customer.
Simple question should be simple to answer. For example, what should do this function, or this part of the API. Use integrated documentation when feature exist.
A good documentation require, examples, responses and explanations about structure or other element.
A tutorial should not be worrying. Browsing to a tutorial is a good place to start. Answer also: what I can do in two minutes, with a quick-start (e.g. one line of code or simple page).
Need to take a way and follow it. You should follow opinion to design it. You should stay with your own definition of things. spread your philosophy in your team and in your products.