That's probably because 'hurry up' is an English idiom. Although, it does mean the same thing. You should try submitting it as an alternative.
Actually, "come" specifies direction (i.e. toward the speaker), whereas "hurry up" doesn't--so there are contexts in which "hurry up" is not the same as "come quickly."
Because it's not about hurrying in general - the verb specifically says "come".
Yeah, because the verb is "come". It's not a generic "do something fast", it's specifically "<sub>Come</sub> fast"
I probably missed something, but since 빨리 is translated as an -ly word, why doesn't it end in 히?