Stetson has been around since 1865; therefore it is very difficult to provide information such as worth, age, or style name for vintage items.
Over the years, many people have used the internet to better identify their Stetson. There have also been many books written about the Stetson hat over the years. We recommend you look into such resources to answer your questions.
For example:
Stetson Hats and the John B. Stetson Company by Jeffrey B. SnyderHat Talk by Debbie Henderson Cowboys & Hatters: Bond Street, Sagebrush, & The Silver Screen by Debbie Henderson