What do they call those chinese button up shirts often worn in Martial arts movies/tv. 1: Are they still in use 2: do they serve a purpose in martial practice
The one pictured can be referred to as a "kung-fu uniform" or "tai-chi uniform".
In practice traditionally no specific uniform is part of tai chi. Modern day practitioners usually wear comfortable, loose T-shirts and trousers made from breathable natural fabrics, that allow for free movement. Despite this, t‘ai-chi ch‘üan has become synonymous with "t‘ai-chi uniforms" or "kung fu uniforms" that usually consist of loose-fitting traditional Chinese styled trousers and a long or short-sleeved shirt, with a Mandarin collar and buttoned with Chinese frog buttons. The long-sleeved variants are referred to as Northern-style uniforms, whilst the short-sleeved, are Southern-style uniforms.
Martial arts uniforms differ depending on the martial art in question. This link provides more details of different types of martial arts attire and their purpose.