I have completed all the icons on the home page. How do I progress to the next level, 12, as there seems to be no new material.
By reviewing and strengthening old lessons as well as participating in immersion. You don't get to the maximum level just by completing the tree.
pseudocreobotra already answered your question but I thought I'd chime in with a bit of additional info: Your level is tied to how many points you have earned, not to how many lessons you have done. Some people review a lot and reach a very high level before they complete the tree. Others, like you, work through the tree quickly and then review.
You'll also gain 'levels' if you try the immersion feature. The levels go up to 25, but they don't mean anything in terms of what you did to get them - they just represent a random number of points.
By the way, the interface in the discussion boards is a bit confusing, but you don't need to type your name - that comes up anyway. It's meant to be a thread heading, and you'll get a better response if you put something like 'Making sense of levels' or 'How does X work?'
Levels are really a motivational device rather than an evaluation measure. Once you've learned everything the course has to offer you there's really no reason even to think about them.