For your first question, the correct response is:
It feared that if Vietnam became communist then surrounding countries would quickly follow.
This reasoning was a key aspect of U.S. foreign policy during the Cold War, specifically concerning containment of communism.
For your second question, the correct response is:
It convinced the United States to become involved in the war.
The domino theory suggested that the fall of one country to communism would lead to the fall of neighboring countries, which influenced U.S. intervention in Vietnam.