Is there proof that exercise helps with anxiety?

Yes: It is known in general that exercise is a great "stress" reducer. Many mood disorders, including anxiety can be helped this way. The use of exercise alone, though may not likely be enough. See a doctor for a more individualized assessment along with exercise.

Yes, there is: The journal of neuroscience published a study in 2013 looking at changes in animal brains as a result of exercise. http://tinyurl.com/mk7on2a the gist here was that running improves anxiety regulation by engaging local inhibitory mechanisms in the ventral hippocampus. This suggests that the brains of exercisers are different -- in more resilient ways -- from others'. http://tinyurl.com/krl4mgu.

Yes: Other people will explain the changes in Lactic Acid meabolism and so forth, insofar as they are understood. It is not a panacea and is no substitute of getting help with difficult life situations, understanding how you may be reacting to situations in ways that are not helpful based on old experience, and otherwise being able to get back in control of your life.