"선생님이 어제 저에게 대답해 줬어요 = The teacher answered me yesterday." 대답하다 means "to answer (someone)", and it's past tense is 대답했다. -아/어 주다 in 대답해 주다 is a helper verb that adds the meaning of "do something for someone". So 선생님이 어제 제게 대답해 줬어요 sounds more natural, like "the teacher kindly answered my question". 대답했어요 in the same phrase would sound stiff, like answering it in a business-like manner. 대답을 줬어요 is not used when referring to a direct verbal answer. 대답/회답/응답을 주다 suggests that the person gives a delayed, formal answer to someone. I'm not sure if this answers all your questions. If not please ask again.

I think you need to understand the expression of give/take. These are natural expressions. 1.선생님이 어제 저에게 대답해 줬어요 (The teacher gave me the answer to me, yesterday.) 2.선생님이 어제 대답했어요. (The teacher answered, yesterday.) - It isn't important to answer WHO. cf) 주다=give 줬어요=gave We prefer to use give/take expression when we say the situation that someone do something to somebody. If we don't need to say [to somebody], we don't say give/take.