> “To ensure that no underage student yields to temptation,” said Dumbledore, “I will be drawing an Age Line around the Goblet of Fire once it has been placed in the entrance hall. Nobody under the age of seventeen will be able to cross this line.”

To answer your questions:

* `could such a thing have happened?`

  Clearly, yes - in theory. The Goblet had no age protection, and the line - as evidenced by Crouch Jr putting in Harry's name - only checked the age of the carrier. NO checks were made to ensure the carrier was the same person as the name on paper. 

  Obviously, none of the wizards ever taken a basic class in computer security.

* `a. Why didn't any of the more adventurous students think of it?`

  No canon answer I'm aware of. 

  Possibly because the only ones likely to try would have been Weasley Twins (or 2-3 others that Dumbledore mentioned to the Twins as having also grown beards :) and the twins had no older student friendly enough to want to risk this.

* `b. Why didn't Dumbledore do something to prevent that from happening?`

  As the quote shows, he did take some steps. 

  Also, **the Goblet was picking a champion from among many entrants - the worthiest one**; and therefore presumably there was very little chance that an under-educated kiddo from Year 2 would be chosen over a senior student as a champion, even if said Year 2 managed to get his name submitted by cheating:

   > Tomorrow night, Halloween, the goblet will return the names of
the three **it has judged most worthy** to represent their schools.

   Why he didn't do more (e.g. match up the name on the slip to the person dropping it), there is no canon info I'm aware of.