Hi! Actually I'm not an art director. I'm the senior concept artist, which pretty much means I draw/paint the neat pictures during the early phases of champ development in order to flesh out the visuals. It's VERY much a team effort at Riot. The champ idea can come from a number of places and is worked on by a number of people in a team. I'm sort of a "floating asset" in that I work on whatever needs to be worked on. If the champ needs to be designed from the ground up, I'll create sketches or thumbnails, then proceed to do more cohesive concepts in more specific presentation. After a considerable amount of iteration on said concept I pass it along to the gents over in 3D via the form of a turnaround, which consists of various views of the champion from which the character's model is made.
The process isn't always linear. I can come in or out of the process at any given time depending on priorities. I pretty do everything you said above aside from supervising. As I said it's a huge team effort, so each of us is welcome to give opinions and ideas to each other, so there isn't a ton of supervision per se, instead a finished product pretty much means that everyone is happy. It's a really amazing atmosphere and supportive environment.
As of now.. and I'm SUPER biased because I worked on her.. my favorite champion is Leona =) However! I'm very fond of Renekton and Tristana. I play a number of them though so I can keep various aspects of the character in mind when I'm designing.