If you weren't rich, or related to a politician, or if you weren't a college student...then you were, quite possibly, headed for Vietnam.
Because university students were exempt from service.
Yes. If the question is regarding a "declared war" or not; there hasn't been a US declared war since WWII. The US Civil War (1861-1865) was not a declared war either.
Rich men could get draft deferments.
Because students were exempt from military service - a serious blunder that killed-off any idea of the educated class as national leaders.
Men of War: Vietnam Trailer
Vietnam War: History and Key Dates
How the Vietnam War Shaped Richard Armitage
Counterinsurgency During the Vietnam War