Q.Cuttings and propagation
I’ve heard a few comments about a trick referred to as “air rooting”. I have a native azalea that is about 6 x 6 feet and must be very old. I found it growing on some land I purchased about 10 years ago. Pics show it is right on the fence line. The bush must be quite old, since it blooms wonderfully in spring. (1) Can it be transplanted? (2) Can I generate a baby from it using the “air rooting” method? Please elaborate on any other care and feeding needs it requires. Thank you.

Transplanting a mature plant like that would be very risky and you could very well lose it. Then you would also lose your opportunity to propagate using "air layering". This article will give you some basics and I'm sure you will find other details on the Internet, including YouTube videos for the process.
https://www.gardeningknowhow.com/garden-how-to/propagation/layering/air-layering-plants.htm