I am not going to answer in a paragraph of 125 words, but I will give you the answer to the first question; The United States didn't want another country to fall to communism. They officially got involved after the attack of the Gulf of Tonkin (U.S destroyers were stationed there and a radio came in that said they had been fired upon by North Vietnamese forces). (45 words BTW).
Americans came to serve in the Vietnam war because of the Military Draft system which as also known as the conscription. It was employed by the federal government of Us in five conflicts: The American Revolution, The American Civil War, Cold War, World War one & two and the Korean War. The draft lasted from 1940 to 1973, in which men were drafted to serve in the military when the posts were could not be filled by voluntary means.
The Draft angered many Americans because it imposed an obligation to serve in the military forces and also because Those having contacts in local boards were able to evade the draft.
The Draft during the Vietnam war worked on birth dates. It functioned through two lotteries. In the first lottery, the birth dates of the candidates who would be called were decided and in the second lottery which was held on the same day as the first one, was used to choose the order of selection.