It all depends on the studio.
dojo
Unfortunately, nowhere. It was built in a studio on set.
When he lived in Michigan his martial art studio was called Fabiano's Karate. Now he's on the XMA Performance Team.
No, it is not rare at all. Almost every small town has at least one karate studio. Most of them are Taekwondo.
karate ka
The Karate costume/uniform is called "Gi".
Karate is practiced in bare feet. The karate uniform is called a gi.
That would usually be a 'studio'
A quick internet search identified the Ultimate Martial Arts Studio and the South Georgia Karate Academy, both in Savannah. There are probably more.
It is called karate in every country, using the name given to it in Okinawa.
yea there is it is called Gin Jan Do KARATE