Once registered in Japan, is the trademark also valid outside Japan?
(Ms. Corporate Owner)

Trademark registration is country specific. A trademark entity registered in Japan, is valid only in Japan.

Once a name has been registered, are the contents of a service falling under the registered name also protected under the same registered name?
(Mr. T. Stylist)

No, the contents of the services are not protected.

Suppose Mr. T registers the name of "Super Style" as a trademark under the services of 'styling', and he has been using a particular method of styling. Nobody can use the name "Super Style." However, as long as a person does not use the name "Super Style", he is free to use the same method as Mr. T, which does not violate Mr. T's trademark right.