JK Rowling has never completely confirmed that Draco actually was a Death Eater, as Harry never receives absolute evidence of Draco's Death Eater status in the books other than various hints of his having a Dark Mark. Draco is therefore never seen with a Death Eater mask in either the books or the films.
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Death the Kid cares about symmetry, because the author wants to make him look like a perfectionist.
No, they hate each other. At the end Harry Potter and Draco Malfoy have come to a sort of civil agreement (probably because Harry saved Draco's life twice and Draco's mother saved Harry), so it is likely Ginny Weasley also has some respect for Draco.
Bellatrix tortured Neville. Severus Snape, his fellow Death-Eaters Amycus and Alecto Carrow, and some wanna-be-Death-Eater Slytherins like Crabbe and Goyle.
Yes, they go to the Yule Ball together and it sorta seems like they're together in The Half-Blood Prince.
Answer: By killing Dumbledore his soul would be ripped apart (like when Voldemort makes horcruxes). It is not the fact that Dumbledore would die, but the fact that Malfoy was about to commit a crime - namely murder - that endangered his soul.