Learn Hardcore Korean: seonsaengnimi jilmuneul deutgo jasehi daedaphae jusyeosseoyo. - The teacher heard my question and answered in detail.

이 is the subject-marking particle used after a noun ending in a consonant. It tells you that 선생님 (teacher) is the one performing the actions (listening and answering).

Why is 듣고 used instead of the past tense 들었어요?

Here -고 is the connective ending that links two actions in sequence: “listening” and then “answering.” If you used 들었어요, you’d have to start a new sentence or use another connector.

Could we use -아서/어서 instead of -고 (i.e. 듣어서)? What’s the difference?

-아서/어서 often implies a causal or direct result (“because/listening and so…”) while -고 simply lists actions in order (“…and then…”). In this case, if you want just sequence without strong cause, 듣고 is more neutral.

What’s 자세히 and why not 자세하게?

Both are adverbs meaning “in detail.” 자세히 is the more common, shorter adverb form. 자세하게 also works but sounds slightly more formal or emphatic.

Why is it 대답해 주셨어요 instead of just 대답했어요?

Two reasons:
1) -아/어 주다 adds a benefactive nuance (“did the favor of answering”).
2) The honorific -시- in 주시다 shows respect to the teacher. So 주셨어요 = “(the teacher) kindly answered (for me/us).”

Which part marks the honorific, and how would the non-honorific version look?

The honorific is the -시- in 주시- (from 주시다). A non-honorific speaker might say 대답해 줬어요 or simply 대답했어요.

Why isn’t 질문을 omitted? Could we say 선생님이 듣고… without it?

You need 질문을 with 을 to mark “the question” as the object of 듣고. Without it, listeners wouldn’t know what was listened to. Omitting it makes the sentence vague.