I told my dad that I want an iphone 6, he bought me this

"chink" is a portmanteau of "chinese" and "north korean". Chi-NK. A cross-breed if you will.
Gook is a generic term for a Korean because they would say "mi gook" to Americans (which means "American"). Apparently it's also applied to Vietnamese because people can't tell the difference between a Korean and Vietnamese.

They're basically like the terms cracker, negro, and wetbacks.

I believe by "negro" you meant "nigger" because "negro" is the more correct term whereas "nigger" is slang.

That term does have a lot of variations.