No. Some infections can cause asthma, but asthma can not be contagious.
No. It is not.
Sort of. Asthma is a polygenetic disease. So, you get it from your parents. Triggers for people who have "underlying" asthma certainly include transmissible disease such as viruses that cause URI. Asthma involves inflammation of the lungs, which is constantly being suppressed during times of good control. With an infection, the suppression mechanism is released and "asthmatic inflammation" follows.