How did Cold War politics lead to the United States fighting in the Vietnam War?

Answer the following questions in at least 3-5 complete sentences each and include supportive details:

What caused the French to withdraw from Vietnam?

Why did the fighting in Vietnam turn into a stalemate by the mid-1960s?

How did Cold War politics lead to the United States fighting in the Vietnam War?

What was the result of the overthrow of Diem in Vietnam?