말하기 전에 생각하세요

Is this literally translated as "think and speak"?

this would translate as "think and speak"--there's no reference to a sequence when using 고 _. It's just a conjunction for verb clauses

Agree. "Think and say."

Better: 말하기 전에 생각하라. (more of a command)

Think and (then) speak.

Is this a Korean phrase? I've never heard any teachers or parents using this.

.