Yes. Asthma can be healed, if the cause of inflammation is reversed: http://bookonhealing.Com/conditions/autoimmune-diseases.Html. Emphysema can't be cured because it is irreversible lung destruction. Smoking causes it, as well as other less common causes. To stop progression, stop smoking and other exposures. Other less common lung conditions may or may not be reversible.
Healing lungs. Yes, if the cause of damage is reversible.
Yes. Just like any other part of your body, the lungs can heal themselves. However, just like your skin (and other parts of the body) if the injury is significant enough, there can be scarring left behind. Since the lungs have a large reserve, only extensive or long-standing injuries to the lungs will generally cause permanent changes to lung function (ex: smoking, autoimmune disease).
Yes. Short answer is yes. The human body is designed to heal from various ailments. However, there is some damage or destruction that is not reversible. For example with the lungs, asthma and COPD can be managed through medications and avoidance of damaging triggers such as cigarette or industrial smoke. Lung damage can be progressive as well. Take care of yourself now, regardless of the past.
Yes. The god given human body has the ability to heal itself from all cure-able ills. Of course there are human ills which are non-curable and some disease which are curable with intervention and appropriate measures can become non-curable by non-compliance with recommendations. Take care of your body - and it will take care of you.