1. Trademark protection is regional. It is a registered trademark in the country where it is located. It is only protected by the country where it is located. The foreign trade company must also have a registered trademark in the country to which it is exported. If the situation as you mentioned occurs, it will be an infringement of counterfeiting a registered trademark.
2. If you encounter this situation again, ask the other party to provide a copy of the trademark registration certificate
3. It depends on whether the foreign trade company has this authority