Yes. Check with your doc first before starting any new exercise program. You may need to use an inhaler pre- and/or post-exercise, especially if you have exercise-induced asthma. Your asthma regimen should be optimized before embarking on any new exercise regimen. All in all, however, exercise is good for asthmatics and your doctor will help you optimize your regimen so exercise is possible.
Yes. Exercising is seldom bad for the lungs - it can optimize oxygen and carbon dioxide exchange across the lungs, which can help people with asthma in the long run. However, some people have exercise induced asthma and would need to pre-treat thenselves with albuterol prior to exercise to prevent exacerbations of such.