How does American immigrant J2 apply for social security number and work card?

You must apply for a work card before you can apply for a social security number.

J2 visa is generally valid for one year, which means that you can travel to and from the United States within one year. As for how long you can stay in the United States, it depends on the J 1 visa, and you can stay until the J 1 visa expires.

American J- 1 visa is a non-immigrant visa, which is issued to all kinds of foreigners who come to the United States to participate in the exchange visit program approved by the State Council. The purpose is to provide educational and cultural exchange opportunities for the United States and other countries, so as to enhance mutual understanding, promote international cooperation and develop friendly relations between countries.