Does Draco actually become a Death Eater?????

Yes he becomes a Death Eater in the sixth book. He complained about a pain in his arm, that it's, obviously, the Dark Mark :)

PS: Voldemort!!!!

yes technically, but even though he bragged about it he never really wanted to, especially during the sixth book, he just couldn't stop the force that was his family obligation... plus he was a pansy who thought he would end up murdered if he went against Voldemort, lol

He does become a Death Eater.

After Lucius Malfoy fails his mission on taking the Prophecy from Potter, he gets jailed in Azkaban, and to take his vengeance, Voldemort commands Draco Malfoy to bring a group of Death Eaters into the school, and kill Dumbledore.