Is it possible to inherit asthma?

Yes. If one parent has asthma a child has about a 25% risk ... If both parents risk is approx. 60%.
Yes &...Yes. Dr. Erman is correct. Asthma is strongly influenced by allergy in childhood & the tendency to develop allergies is inherited. 95% of children older than 3 years who have asthma also have allergies. That number is around 50% for adults with asthma. Smoking during pregnancy is another major cause of asthma in children irrespective of a family history of allergy or asthma.
Yes. You can inherit the tendency for atopic, or allergic-type diseseas, which is one of the causes of asthma.