(Note: This is NOT an official United States Government website)
The Coast Guard was formed, as the Revenue Cutter Service, on August 4th, 1790. It became the "Coast Guard" January 28th, 1915 when the Revenue Cutter Service was merged with the National Lifesaving Service. Today the Coast Guard reports to the Department of Homeland Security.
It's in New London, CT.
No, the Coast Guard Academy accepts applicants via competitive exam. They admit about 300 new students per class.
Actually the Coast Guard has a wide range of missions including patrolling the U.S. coastal waters, doing ocean rescue and even drug interdiction. Coast Guard ships have even been involved in assisting with patrol in foreign waters during wartime; off the coast of Vietnam and in the Persian Gulf.
Start here: http://www.gocoastguard.com/
O1 - Ensign
O2 - Lieutenant Junior Grade
O3 - Lieutenant
O4 - Lieutenant Commander
O5 - Commander
O6 - Captain
O7 - Rear Admiral, Lower Half
O8 - Rear Admiral, Upper Half
O9 - Vice Admiral
O10 - Admiral
A cutter is any Coast Guard ship longer than 65 feet and with accommodations for the crew to live aboard.
The Eagle is a Barque - a 3-masted sailing ship that was originally part of the Reichsmarine (German navy) during WWII as a training and supply ship. Captured by the U.S. after the war it was commissioned as a U.S. Coast Guard training ship in 1946 and has remained so ever since. Home ported at New London, Connecticut. Though it is a sailing ship it also has an auxiliary diesel engine.