Pretty sure that they are aware that they are taking a "test", but they are not aware that they had no chance of succeeding - after all, Lt. Saavik had stated that she was not prepared for the no-win scenario. After all, the element of surprise had much to do with the difficulty of the test.
I would guess that cadets take several different tests with different outcomes and have no idea what test was coming next. As stated above, the surprise element was as important as the difficulty. The typical cadet also may only take 8-10 tests out of say maybe 25 or 30 possible test, so it could be that not every cadet takes the Kobaysahi Maru test.
FInally, I would bet a million bars of latium that if the Kobayashi Maru test is still given to cadets, the name of the ship itself and probably many background elements change each time the time is given. Since the Maru Test seems to be common knowledge, the first mention of the "Kobayashi Maru" would signal what the test was. It could be they use the name Kobayashi Maru for every ship in every test but then the no-win scenario test would be referred to by a different name.
Tuvok gave the Maquis aboard Voyager a version of the test.
It seems unlikely that a no-win scenario could go even one semester before word of mouth (i.e. cadets sharing thier results) would cntaminate the results of subsequent tests. It seems logical that the test is varied significantly from time to time, to update it for new technology and political situations (it would seem sill for cadets during the Dominion War to accept Klingon ships as the enemy when the Empire was a close ally at the time) as well as change it enough so that cadets couldn't figure out a way to win the no-win scenario by comparing notes. I rather suspect that there are multiple versions given at a time, much like you high school science teacher probably gave multiple versions of a multiple choice test so that students can't cheat off of each other. Thusly, if there are multiple versions, a cadet probably would not realize which test was supposed to be the no-win scenario until he or she failed it. It seems that the Kobyashi Maru is infamous enough that it's name seems to have entered 24th century lexicon as slang for a no-win scenario.
They are, although they are probably not told that it is a true and absolute no-win scenario. This would inspire cadets to continue to challenge themselves in what must be one of Starfleet Academy's most prominent signature learning and preparatory experiences. Another of Roddenberry's "Japanophile" references. It may be named after the Japanese astronomer Toru Kobayashi, or the Japanese motion-picture director Masaki Kobayashi, who is responsible for a very famous Japanese film trilogy about life in WWII-era fascist Japan (fascism being a story premise and story element Star Trek has taken up more than once). The "Maru" suffix-word is a Japanese ship-naming convention.
The meme may be meant to elicit the memory of a Japanese fishing trawler, the Daigo Fukuryu Maru ("Ship of the Lucky Dragon") which was a doomed ship--although this was unknown to the crew at the time. The crew ultimately died of acute radiation poisoning as a result of intensely-radioactive nuclear fallout ("the death ash") from the United States' Castle Bravo thermonuclear device test, which occured at Bikini Atoll, in the south-Pacific archipelago of the Marshall Islands, on March 1, 1954. Theirs was certainly a no-win scenario ProfessorTrek 05:27, September 7, 2011 (UTC)