I'm going to tell you straight up they're not gonna know what weave is. You'd have to explain the process of getting it done Ironic because all the beauty supply owners are korean I know haha But like Heesob said, braid is 땋은 머리 cornrow... if they know it its 콘로, but again they probably won't so you'd have to explain it like heesob said and say 여러 가닥으로 딴 머리(more than likely you're gonna have to show a picture though) twists are 꼬단 머리 or just 트위스트한 머리 (you might have to show a picture of this too to get your point across)

Braids => 땋은 머리 cornrows => 여러 가닥으로 딴 머리 , 콘로 twist => 꼬다, 비틀다 weave => 짜다, 뜨다, 엮다