Doing Business As

Dear officer

Regarding, the question about the 'DBA'. Here is the status.

I registed a copmany as a c corporation in USA.

1. Can I using another foreign company name for doing business in U.S.? (the foreign company authorized me to use their compnay name for selling their product in U.S.)

2. In order to protect the foreign company business name, Can the foreign company register their trademark by themself ? 

thank you very much