Students learn to discuss mathematics. They become aware of multiple approaches of solving a problem. They learn to work longer on a problem. Homework done as described in question 9 above has led to a significant improvement in the students ability to make clear written presentations of their mathematical thoughts. Students who have had to make presentations of new material to the class have a much better understanding of that material than if they sit and listen to me lecture.
Fragile students benefit the most.
In some course, especially proof oriented course, I think that students become more comfortable with abstract thought. It is my feeling that they enjoy mathematics more. The overall results are generally better than when the students did the same, or comparable things, themselves. The only change I see visibly is the acknowledgement that doing mathematics need not be a solitary activity. They become better thinkers.