Thank you so much! Asthma is per se not an allergy. It is a chronic (permanent) inflammation of the airways, which can every now and then cause them to react and become spastic (tight). The cause of that inflammation / irritation can be an allergy (to pollen for example), but there are other possible causes.
As to your second question, it's a very good one with a very complex answer which I won't dare to try to explain, at least without a lot of prior research. Basically the immune system reacts to peanuts the same way it would react to a parasite, but it's not even 100% known why. The part that is known is complex immunology which I don't dare to get into now (maybe in a future article).